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PUBLICATIONS

  1. Extension of Baker's analogue of Littlewood's diophantine approximation problem, Kodai Math. J. 14  (1991), 335--340.

  2. On the characteristic word of the inhomogeneous Beatty sequence, Bull. Austral. Math. Soc. 51 (1995), 337--351.

  3. The fractional part of nθ+φ and Beatty sequences, J. Theorie des Nombres de Bordeaux 7 (1995), 387--406.

  4. A certain power series and the inhomogeneous continued fraction expansions, J. Number Theory 59 (1996), 291--312.

  5. A certain power series associated with a Beatty sequence, Acta Arith. 76 (1996), 109--129.

  6. (with A. J. van der Poorten) Substitution invariant Beatty sequences, Japan. J. Math. 22 (1996), 349--354.

  7. The sum of consecutive fractional parts, Tsukuba J. Math. 21 (1997), 129--137.

  8. On inhomogeneous continued fraction expansion and inhomogeneous Diophantine approximation, J. Number Theory 62 (1997), 192--212.

  9. On inhomogeneous Diophantine approximation and the Nishioka-Shiokawa-Tamura algorithm, Acta Arith. 86 (1998), 305--324.

  10. Substitution invariant inhomogeneous Beatty sequences,Tokyo J. Math. 22 (1999), 235--243 . 　

  11. On inhomogeneous Diophantine approximation and the NST algorithm, Developments in Math. 2 (1999),241--251= 'Number Theory and its Applications', ed. by K. Gyory and S. Kanemitsu, Kluwer Academic.

  12. On inhomogeneous Diophantine approximationwith some quasi-periodic expressions, Acta Math.Hung. 85 (1999), 311--330. 　

  13. On inhomogeneous Diophantine approximationwith some quasi-periodic expressions II, J. Theorie des Nombres de Bordeaux 11 (1999), 331--344.

  14. Continued fractions and Newton's approximations, Math. Communications 4 (1999),167--176. 　

  15. On palindromic sequences from irrational numbers, Fibonacci Quart. 39 (2001), 66--74.

  16. Continued fractions and Newton's approximations II, Fibonacci Quart. 39 (2001), 336--338.

  17. (with M. Beck and I. M. Gessel)The polynomial part of a restricted partition function related to the Frobenius problem, Electronic. J. Combinatorics 8 (No.1) (2001), #N7.

  18. An approximation property of quadratic irrationals, Bull. Soc. Math. France 135  (2002),  35--48.

  19. On inhomogeneous Diophantine approximationand the Borweins'algorithm II, Developments in Math. 6 (2002), 223--242= 'Analytic Number Theory', ed. by C. Jia and K. Matsumoto, Kluwer Academic.

  20. The interval associated with a Fibonacci number, Fibonacci Quart. 41 (2003), 3--6.

  21. On Tasoev's continued fractions, Math. Proc. Cambridge Philos. Soc. 134 (2003), 1--12.

  22. On Hurwitzian and Tasoev's continued fractions, Acta Arith. 107 (2003),161--177.

  23. Simple continued fraction expansions of some values of certain hypergeometric functions, Tsukuba J. Math. 27 (2003), 161--173.

  24. On the number of solutions of the Diophantine equation of Frobenius--General case, Math. Communications 8 (2003), 195--206.

  25. Recurrence relations of the leaping convergents, JP J. Algebra Number TheoryAppl. 3 (2003), 447--459.

  26. On inhomogeneous Diophantine approximationand the Borweins'algorithm,Far East J. Math. Sci. (FJMS) 12 (2004), 203--224.

  27. Arithmetic properties of the leaping convergents of e1/s,Tokyo J. Math. 27 (2004), 1--12.

  28. Tasoev's continued fractions and Rogers-Ramanujan continued fractions, J. Number Theory, 109 (2004), 27--40.

  29. Rational approximations to Tasoev continued fractions, Math. Pannon. 15 (2004),199--207.

  30. On a Zaremba's conjecture for powers, Sarajevo J. Math. 1(13) (2005) , 9--13.

  31. Rational approximations to Tasoev continued fractions,II, Liet. Mat. Rink. 45 (2005), 84--94.

  32. Hurwitz and Tasoev continued fractions,Monatsh. Math. 145 (2005), 47--60.

  33. An algorithm of infinite sums representations and Tasoev continued fractions, Math. Comp. 74 (2005), 2081--2094.

  34. Some recognizable forms of simple continued fractions, International J.Math. Sci. 4 (2005), 47--63.

  35. Hurwitz and Tasoev continued fractions with long period,Math. Pannon. 17 (2006), 91--110.

  36. Some recognizable forms of simple continued fractions,II,Rev. Roum. Math. Pures Appl.(RRMPA) 51 (2006), 219--238.

  37. Continued fraction of e2 with confluent hypergeometric functions,Liet. Mat. Rink. 46 (2006), 513--531.

  38. A proof of the continued fraction expansion of e^(2/s), Integers 7 (2007), #A30 (8 pages).

  39. Some combinatorial properties of the leaping convergents,Combinatorial Number Theory , Proceedings of the Integers Conference 2005 in Celebration of the 70th Birthday of Ronald Graham, Carrollton, Georgia, USA, October 27--30,2005, eds. by B. M. Landman, M. B. Nathanson, J. Nesetril, R. J. Nowakowski and C. Pomerance, Walter de Gruyter, 2007, pp.315--325.= Integers 7(2) (2007), #A21 (10 pages).

  40. Hurwitz continued fractions with confluent hypergeometric functions, Czech. Math. J. 57 (2007), 919--932.

  41. (with C. Elsner and I. Shiokawa) Approximation of values of hyperbolic functions by restricted rationals, J. Theorie des Nombres de Bordeaux 19 (2007), 393--404.

  42. (with C. Elsner)A recurrence formula for leaping convergents of non-regular continued fractions, Linear Algebra Appl. 428 (2008), 824--833.

  43. Heron's square root approximations, JP J. Algebra Number Theory Appl. 10 (2008), 81--88.

  44. Tasoev continued fractions with long period, Far East J. Math. Sci. (FJMS) 28 (2008), 89--121.

  45. (with C. Elsner)On the residue classes of integer sequences satisfying a linear three-term recurrence formula, Linear Algebra Appl. 429 (2008), 933--947.

  46. More on Hurwitz and Tasoev continued fractions, Sarajevo J. Math. 4 (2008), 155--180.

  47. Shrinking the period length of quasi-periodic continued fractions, J. Number Theory 129 (2009), 358 - 366.

  48. A Diophantine approximation of e^(1/s) in terms of integrals, Tokyo J. Math. 32 (2009), 159--176.

  49. Diophantine approximations of tanh, tan, and linear forms of e in terms of integrals, Rev. Roum. Math. Pures Appl. (RRMPA) 54 (2009), 223--242.

  50. (with C. Elsner and I. Shiokawa)On convergents formed from Diophantine equations, Glasnik Mat. 44 (2009), 267--284.

  51. On continued fraction expansions of Fibonacci and Lucas Dirichlet series, Fibonacci Quart. 46/47 (2008/2009), 268--278.

  52. (wtih C. K. Caldwell) Some periodicities in the continued fraction expansions of Fibonacci and Lucas Dirichlet series, Fibonacci Quart. 48 (2010), 47--55.

  53. (with T. Chaichana and V. Laohakosol) Liouville numbers in non-Archimedean situation, Publ. Math. Debrecen 77 (2010) 39--63.

  54. Some combinatorial properties of the leaping convergents, II, Applications of Fibonacci Numbers, (Proceedings of the 12th International Conference on Fibonacci Numbers and their Applications), Congr. Numer. 200 (2010) , 187--196.

  55. (with V. Laohakosol) On the sum of reciprocal numbers satisfying a recurrence relation of order s, J. Integer Seq. 13 (2010), Article 10.5.8 (9 pages).

  56. Four-term leaping recurrence relations, Linear Multilinear Algebra 58 (2010), 875--886.

  57. (wtih C. K. Caldwell)Powers of Sierpinski numbers base b, Integers 10 (2010), 423--436.

  58. Sequences Hn for which Hn/Hn+1 approaches an irrational number, Fibonacci Quart. 48 (2010), 265--275.

  59. (with V. Laohakosol and P. Ruengsinsub) Independence measures of arithmetic functions, J. Number Theory 131 (2011), 1--17.

  60. (with S. H. Holliday) On the sum of reciprocal generalized Fibonacci numbers, Integers 11A (2011), 441--455.

  61. On the sum of reciprocal Tribonacci numbers, Ars Combin. 98 (2011), 447--459.

  62. On the nearest integer of the sum of the reciprocal Fibonacci numbers, Applications of Fibonacci Numbers, (Proceedings of the 14th International Conference on Fibonacci Numbers and their Applications), Aportaciones Matematicas Investigacion 20 (2011),171--184.

  63. Leaping convergents of Hurwitz continued fractions, Discuss. Math. Gen. Algebra Appl. 31 (2011),101--121.

  64. Leaping convergents of Tasoev continued fractions, Discuss. Math. Gen. Algebra Appl. 31 (2011),201--216.

  65. (with V. Laohakosol and P. Ruengsinsub) Independence measures of arithmetic functions II, Acta Arith. 153 (2012),199--216.

  66. Congruent numbers and continued fractions, Fibonacci Quart. 50 (2012), 222--226.

  67. Linear recurrence relations associated with multinomial Pascal triangles, Math. Pannon. 23 (2012),135--146.

  68. Linear recurrence relations associated with multinomial Pascal triangles II, Far East J. Math. Sci. (FJMS) 67 (2012), 153--180.

  69. Some exact algebraic expressions for the tails of Tasoev continued fractions, J. Austral. Math. Soc. 92 (2012), 179--193.

  70. (with K. Liptai and L. Szalay) Some relationships between poly-Cauchy type numbers and poly-Bernoulli type numbers, East-West J. Math. 14 (2012), 114--120.

  71. On convergents of certain values of Tasoev continued fractions associated with Diophantine equations, Mat. Metodi Fiz.-Mekh. Polya 55 (2012), 16--22. = J. Math. Sci. (N.Y.) 192 (2013), 498--505.

  72. (with F. Luca and Y. Tachiya) On the multiplicative order of $F_{n+1}/F_n$ modulo $F_m$, Integers 12B (2012/2013), #A8 (13 pages).

  73. Poly-Cauchy numbers, Kyushu. J. Math. 67 (2013), 143--153.

  74. (with K. Betsumiya, M. Hirasaka, and A. Munemasa) Upper bounds on cyclotomic numbers, Linear Algebra Appl. 438 (2013), 111--120.

  75. Poly-Cauchy numbers with a q parameter, Ramanujan J. 31 (2013), 353--371.

  76. (with J. J. Bravo and F. Luca) On the distance between products of consecutive Fibonacci numbers and powers of Fibonacci numbers, Indag. Math. 24 (2013), 181--198.

  77. Hypergeometric Cauchy numbers, Int. J. Number Theory 9 (2013), 545--560.

  78. (with T. Chaichana and V. Laohakosol) On convergents of certain values of hyperbolic functions formed from Diophantine equations, Tokyo J. Math. 36 (2013), 239--251.

  79. Sums of products of Cauchy numbers, including poly-Cauchy numbers, J. Discrete Math. 2013 (2013), Article ID 373927, 10 pages.

  80. (with F. Luca) Some relationships between poly-Cauchy numbers and poly-Bernoulli numbers, Ann. Math. Inform. 41 (2013), 99--105.

  81. (with K. Kamano) Poly-Cauchy polynomials, Mosc. J. Comb. Number Theory 3 (2013), 181--207.

  82. (with V. Laohakosol and K. Liptai)A generalization of poly-Cauchy numbers and their properties, Abstract Appl. Anal. 2013 (2013), Article ID 179841, 8 pages.

  83. Explicit formulae for sums of products of Cauchy numbers including poly-Cauchy numbers, RIMS Kokyuroku Bessatsu B46 (2014), 187--203.

  84. Some generalized Fibonacci identities including powers and binomial coefficients, Fibonacci Quart. 52 (2014), 50--60.

  85. (with K. Kamano) Explicit formulae for sums of products of Bernoulli polynomials, including poly-Bernoulli polynomials, Ramanujan J. 33 (2014), 301--313.

  86. (with K. Kamano) Some congruence relations of poly-Cauchy numbers, J. Comb. Number Theory 5 (2014), 145-150.

  87. (with H. Belbachir and L. Szalay) Linear recurrences associated to rays in Pascal's triangle and combinatorial identities, Math. Slovaca 64 (2014),287-300.

  88. Sums of products of Cauchy polynomials, including poly-Cauchy polynomials, J. Algerian Math. Soc. 1 (2014), Article #2 (12 pages).

  89. (with G. Shibukawa) Poly-Cauchy polynomials and generalized Bernoulli polynomials, Acta Sci. Math. (Szeged) 80 (2014),373--388.

  90. (with L. Szalay) Balancing with binomial coefficients, Int. J. Number Theory 10 (2014), 1729--1742.

  91. (with Florian Luca and Claudio Pita) A note on the denominators of Bernoulli numbers, Proc. Japan Acad. Ser.A 90 (2014), 71--72.

  92. (with Dae San Kim, Taekyun Kim and Jong-Jin Seo) Barnes' multiple Frobenius-Euler and poly-Bernoulli mixed-type polynomials, Adv. Difference Equ. (2014) 2014:92, 16 pages. 

  93. (with L. Szalay) Shifted poly-Cauchy numbers, Lithuanian Math. J. 54 (2014), 166--181.

  94. Convolution identities for Cauchy numbers, Acta Math. Hungar. 144 (2014), 76--91.

  95. (with Florian Luca and Claudio Pita) Generalized poly-Cauchy polynomials and their interpolating functions, Colloq. Math. 136 (2014), 13--30.

  96. (with Dae San Kim, Taekyun Kim and Sung-Hun Lee) Barnes-type Daehee of the first kind and poly-Cauchy of the first kind mixed-type polynomials, Adv. Difference Equ. (2014) 2014:140, 22 pages.

  97. (with Dae San Kim, Taekyun Kim and Jong-Jin Seo) Barnes-type Daehee polynomials, Adv. Difference Equ. (2014) 2014:141, 26 pages.

  98. (with Dae San Kim, Taekyun Kim and Hyuck In Kwon) Barnes' multiple Bernoulli and generalized Barnes' multiple Frobenius-Euler mixed-type polynomials, Adv. Difference Equ. (2014) 2014:238, 16 pages.

  99. (with Omar Khadir) An integer sequence for solving the modular equation 3^x\equiv b [p] when p is prime, J. Theor. Phys. Crypt. 7 (2014), 11—19, Article #4.

  100. (with Zuzana Masakova and Edita Pelantova) Higher-order identities for Fibonacci numbers, Fibonacci Quart. 52, no.5 (2014), 150--163. 

  101. Sums of products of Cauchy numbers, including generalized poly-Cauchy numbers, Tokyo J. Math. 38 (2015) 45--74.

  102. Convolution identities for Cauchy numbers of the second kind, Kyushu. J. Math. 69 (2015), 125--144.

  103. (with Mitsugu Hirasaka) On computation of arbitrary integer powers for certain type of band matrices with Fibonacci numbers, J. Comb. Number Theory 7 (2015), 65—78.

  104. (with Dae San Kim, Taekyun Kim, Seog-Hoon Rim) Multi-poly-Cauchy polynomials, J. Comput. Anal. Appl. 18 (2015), 536--550.

  105. (with Taekyun Kim, Sang-Hun Lee and Jong-Jin Seo) q-poly-Cauchy numbers associated with Jackson integral, J. Comput. Anal. Appl. 18 (2015), 685--698.

  106. (with Dae San Kim, Taekyun Kim and Jong-Jin Seo) An umbral calculus approach to poly-Cauchy polynomials with a q parameter, J. Comput. Anal. Appl. 18 (2015), 762--792.

  107. (with Dmitry V. Dolgy, Dae San Kim, Taekyun Kim and Sang-Hun Lee) Barnes' multiple Bernoulli and poly-Bernoulli mixed-type polynomials, J. Comput. Anal. Appl. 18 (2015), 933—951.

  108. (with Dae San Kim, Taekyun Kim and Jong-Jin Seo) Barnes-type Narumi of the first kind and Barnes-type Peters of the first kind hybrid polynomials, J. Comput. Anal. Appl. 19 (2015), 1012--1037.

  109. (with Mehmet Cenkci) Poly-Bernoulli numbers and polynomials with a q parameter, J. Number Theory 152 (2015), 38--54.

  110. Higher-order convolution identities for Cauchy numbers of the second kind, Proc. Jangjeon Math. Soc. 18 (2015), 369--383.  

  111. (with Hassan Jolany and Robert B. Corcino) More properties on multi-poly-Euler polynomials, Bol. Soc. Mat. Mex. 21 (2015), 149--162.　

  112. (with Dae San Kim, Taekyun Kim and Dmitry V. Dolgy) Barnes-type degenerate Bernoulli polynomials, Adv. Stud. Contemp. Math. 25 (2015), 121--146.

  113. (with Taekyun Kim, Dae San Kim and Sang-Hun Lee) Higher-order  Daehee of the second kind and poly-Cauchy of the second kind mixed-type polynomials, J. Nonlinear Convex Anal. 16 (2015), 1993 —2015.

  114. q-poly-Bernoulli numbers and q-poly-Cauchy numbers with a parameter by Jackson's integrals, Indag. Math. 27 (2016), 100 —111.

  115. (with I. Mezo), Several explicit formulae of Cauchy polynomials in terms of r-Stirling numbers, Acta Math. Hungar. 148 (2016), 522 —529.

  116. (with I. Mezo and L. Szalay), Incomplete Cauchy numbers, Acta Math. Hungar. 149 (2016), 306 —323.  DOI:10.1007/s10474-016-0616-z

  117. Incomplete poly-Cauchy numbers, Monatsh. Math. 180 (2016), 271 —288.   

  118. (with Dae San Kim, Taekyun Kim, Jong-Jin Seo and Seog-Hoon Rim) Barnes-type Narumi of the Second Kind and Poly-Cauchy of the Second Kind Mixed-Type Polynomials, J. Comput. Anal. Appl. 20 (2016), 91—120.

  119. (with Dae San Kim, Taekyun Kim, H. I. Kwon and Sang-Hun Lee) Barnes-type Peters polynomials associated with　poly-Cauchy polynomials of the second kind, J. Comput. Anal. Appl. 20 (2016), 151—174.  

  120. (with Dae San Kim, Taekyun Kim and Dmitry V. Dolgy) Barnes-type Peters of the first kind and　poly-Cauchy of the first kind mixed-type polynomials, J. Comput. Anal. Appl. 20 (2016), 803—825.  

  121. Higher-order convolution identities for Cauchy numbers, Tokyo J. Math. 39 (2016), 225—239.

  122. (with K. Liptai and I. Mezo) Incomplete poly-Bernoulli numbers associated with incomplete Stirling numbers, Publ. Math. Debrecen 88 (2016), 357—368.

  123. (with Charles K. Cook) Some identities for sequences of binomial sums of generalized Fibonacci numbers, Fibonacci Quart. 54 (2016), 105--111.

  124. (with Yuri Bilu, Florian Luca, Amalia Pizarro-Madariaga and Pantelimon Stanica)On a divisibility relation for Lucas sequences, J. Number Theory 163 (2016), 1—18.   

  125.  (with Hajime Kaneko) Cauchy-Carlitz numbers, J. Number Theory163 (2016), 238--254.  

  126. (with Yilmaz Simsek) Third and higher order convolution identities for Cauchy numbers, 30 (2016), 1053--1060. 

  127. (with Claudio de J. Pita Ruiz V.) Several explicit formulae for Bernoulli polynomials, Math. Communications 21 (2016), 127--140.  

  128. (with Laszlo Szalay) q-multiparameter-Bernoulli polynomials and q-multiparameter-Cauchy polynomials by Jackson's integrals, Integers 16 (2016), #A39, 11 pages.

  129. (with Robert B. Corcino, Hassen Jolany and Cristina B. Corcino) On generalized multi poly-Euler polynomials, Fibonacci Quart. 55 (2017), 41--53.

  130. Generalized incomplete poly-Bernoulli and poly-Cauchy numbers, Period. Math. Hungar. 75 (2017), 96—113.

  131. (with Florian Luca) Generalized incomplete poly-Bernoulli polynomials and generalized incomplete poly-Cauchy polynomials, Int. J. Number Theory March 13 (2017), 371--391. 　

  132. (with Feng-Zhen Zhao) The log-convexity of the poly-Cauchy numbers, Quaest. Math. 40 (2017), 39--47.　

  133. Complementary Euler numbers,  Period. Math. Hungar. 75 (2017), 302--314.　

  134.  (with Abdelmejid Bayad) New characterization of Appell polynomials,Integral Transforms Spec. Funct. 28 (2017), 212—222.

  135.  (with Eda Yuluklu and Yilmaz Simsek) Identities related to special polynomials and combinatorial numbers, Filomat 31 (2017), 4833--4844. 

  136. (with Paul Thomas Young) Exact p-adic valuations of Stirling numbers of the first kind, J. Number Theory  177 (2017), 20—27.

  137. (with Jose Luis Ramirez) Incomplete poly-Bernoulli numbers and incomplete poly-Cauchy numbers associated to the q-Hurwitz-Lerch zeta function, Mediterr. J. Math. 14 (2017), Art. 133, 19 pp.            

  138. (with Pingzhi Yuan) Hypergeometric Cauchy numbers and polynomials, Acta Math. Hungar. 153  (2017), 382--400.   

  139. (with Jose Luis Ramirez) Generalized poly-Cauchy and poly-Bernoulli numbers by using incomplete r-Stirling numbers, Aequationes Math. 91  (2017), 1055—1071. 

  140. (with Jose Luis Ramirez and Victor F. Sirvent) Multi-poly-Bernoulli numbers and polynomials with a q parameter, Lithuanian Math. J. 57 (2017), 490—505.  

  141. (with Yilmaz Simsek) Identities related to the Stirling numbers and modified Apostol-type numbers on umbral calculus, Miskolc Math. Notes 18 (2017), 905—916..

  142. Convolution identities for Tribonacci numbers, Ars Combin. 136 (2018), 199--210.

  143. (with Paul Thomas Young) Generalized Stirling numbers with poly-Bernoulli and poly-Cauchy numbers, Int. J. Number Theory 14  (2018), 1211--1222.

  144.  (with Laszlo Szalay) A new formula for hyper-Fibonacci numbers, and the number of occurrences, Turkish J. Math. 42 (2018), 993--1004. 

  145. (with Laszlo Nemeth and Laszlo Szalay) Tilings of hyperbolic (2 x n)-board with colored squares and dominoes, Ars Math. Contemp. 15 (2018), 337--346. 　

  146. (with Claudio de J. Pita Ruiz V.) Truncated Euler polynomials, Math. Slovaca 68 (2018), 527--536.  

  147. (with Gopal Krishna Panda and Ravi Kumar Davala) Reciprocal sums of sequences involving balancing and Lucas-balancing numbers, Math. Rep. (Bucur.) 20 (2018), 201--214.

  148. (with Clark Kimberling, Kalman Liptai and Laszlo Szalay) A connection between hyper-Fibonacci numbers and fissions of polynomial sequences, Fibonacci Quart. 56 (2018), 195—199.

  149. (with Abdelmejid Bayad) Zeta functions interpolating the convolution of the Bernoulli polynomials,Integral Transforms Spec. Funct. 29 (2018), 611--622. 　　　　

  150. Incomplete multi-poly-Bernoulli numbers and multiple zeta values, Bull. Malays. Math. Sci. Soc. 41 (2018), 2029--2040.               

  151. (with Jose Luis Ramirez) Some determinants involving incomplete Fubini numbers, An. Stiint. Univ. ``Ovidius'' Constanta Ser. Mat. 26 (2018),no.3, 143--170.

  152. (with Pinthira Tangsupphathawat and Vichian Laohakosol) Minimal polynomials of algebraic cosine values, II, J. Integer Seq. 21 (2018), Article 18.9.5, 11 pages.

  153. (with Claudio de J. Pita Ruiz V.)Some formulas for Bell numbers, Filomat 32 (2018) no.11, 3881--3889.

  154. (with Bijan Kumar Patal and Prasanta Kumar Ray) Higher-order identities for the second-order sequence, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 64 (2018) no.2, 357--368. 

  155. (with Hajime Kaneko) Bernoulli-Carlitz and Cauchy-Carlitz numbers with Stirling-Carlitz numbers, RIMS Kokyuroku Bessatsu B72 (2018), 23–35.    

  156. Leaping Cauchy numbers, Filomat 32 (2018) no.18, 6167--6176.

  157. Truncated Bernoulli-Carlitz and truncated Cauchy-Carlitz numbers, Tokyo J. Math. 41 (2018), 541–556. 

  158. (with Rupam Barman) Lehmer’s generalized Euler numbers in hypergeometric functions, J. Korean Math. Soc. 56 (2019), 485–505. https://doi.org/10.4134/JKMS.j180227

  159. (with Rusen Li) Convolution identities for Tribonacci numbers with symmetric formulae, 21 (2019), 27--47.

  160. (with Amalia Pizarro-Madariaga) Harmonic numbers associated with inversion numbers in terms of determinants, Turkish J. Math. 43 (2019), 340--354.

  161. (with Miho Aoki and Gopal Krishna Panda) Several properties of hypergeometric Bernoulli numbers, J. Inequal. Appl. 2019 (2019), Paper No.113. 24p.

  162. (with Pallab Kanti Dey) Some identities of Cauchy numbers associated with continued fractions, 74 (2019), 74:83.

  163. Convolution identities for Tribonacci-type numbers with arbitrary initial values, Palestine J. Math. 8 (2019), 413--417.

  164. (with Roberto B. Corcino, Hassan Jolany, Cristina B. Corcino) On multi poly-Bernoulli polynomials, J. Inequal. Spec. Func. 10 (2019), No.2, 21--34.

  165. (with Rusen Li) Convolution identities for Tetranacci numbers, Notes Number Theory Discrete Math. 25 (2019), no.3, 142--169. 

  166. Some recurrence relations of poly-Cauchy numbers, J. Nonlinear Sci. Appl. 12 (2019), 829—845.  http://dx.doi.org/10.22436/jnsa.012.12.05

  167. (with Vichian Laohakosol and Jittinart Rattanamoong) Complex Cantor series, Cantor products and their independence, Integers 19 (2019) #57, 21 pages.

  168. (with Vichian Laohakosol and Pinthira Tangsupphathawat) Truncated Euler-Carlitz numbers, Hokkaido Math. J. 43 (2019), 569--588.

  169. (with Wenpeng Zhang) Several properties of multiple hypergeometric Euler numbers, Tokyo J. Math. 42 (2019), 551--570. 

  170. (with Claudio de J. Pita Ruiz V.) Shifted Cauchy numbers, Quaest. Math. 43 (2020), 213--226.   

  171. (with Huilin Zhu) Hypergeometric Euler numbers, AIMS Math. 5 (2020), 1284--1303. 

  172. (with Bijan Kumar Patal and Prasanta Kumar Ray) On the periodicity of Lucas-balancing numbers and $p$-adic order of balancing numbers, Iran. J. Sci. Technol. Trans. A Sci. 44  (2020), 557—562.  

  173. On poly-Euler numbers of the second kind, RIMS Kokyuroku Bessatsu  B77 (2020), 143--158.  

  174. Two types of hypergeometric degenerate Cauchy numbers, Open Math. 18 (2020), 417--433. https://doi.org/10.1515/math-2020-0030

  175. A parametric type of Bernoulli polynomials with level 3, Rev. R. Acad. Cienc. Exactas Fis. Nat., Ser. A Mat., RACSAM, 114 (2020), Article No.151. 19p. 

  176. (with Jose Luis Ramirez) Convolutions of bi-periodic Fibonacci numbers, Hacet. J. Math. Stat. 49 (2020), 565--577.  DOI:10.15672/hujms.568340  

  177. (with Claudio Pita-Ruiz) Poly-Cauchy numbers with level 2, Integral Transforms Spec. Funct. 31 (2020), 570—585.   https://doi.org/10.1080/10652469.2019.1710745

  178. (with Yanapat Tongron) Explicit formulae for some sums of trinomial coefficients, Sci. Tech. RMUTT J. 10 (2020), 161--169.    Currently, Prog. Appl. Sci. Tech. (PAST)

  179. Branched continued fractions associated with Hosoya index of the tree graph, MATCH Commun. Math. Comput. Chem. 84 (2020), 399--428.  

  180. (with Jose Luis Ramirez and Victor F. Sirvent) A (p,q)-analogue of poly-Euler polynomials and some related polynomials, Ukrainian Math. J. 72 (2020) no.4, 467--482.  

  181. Higher-order identities for balancing numbers, Notes Number Theory Discrete Math. 26 (2020), no.3, 71--84.

  182. (with Wenpeng Zhang) Several expressions of truncated Bernoulli-Carlitz and truncated Cauchy-Carlitz numbers, AIMS Math. 5 (2020), 5939--5954.

  183. Continued fraction expansions of the generating functions of Bernoulli and related numbers, Indag. Math. 31 (2020), 695--713. 

  184. Shifted Bernoulli numbers and shifted Fubini numbers, Linear Nonlinear Anal. (2020), 245--263.

  185. (with Asim Patra and Gopal Krishna Panda) The growth rate of random sequences, Proc. Jangjeon Math. Soc. 23 (2020), no. 3, 297--304.

  186. Fibonacci determinants with Cameron's operator, Bol. Soc. Mat. Mex. 26 (2020), No. 3, 841--863.

  187. (with Su Hu) Explicit expressions for the related numbers of higher order Appell polynomials, Quaest. Math. 43 (2019), 1019--1029. 

  188. Hypergeometric degenerate Bernoulli polynomials and numbers, Ars Math. Contemp. 18 (2020), 163--177.     https://doi.org/10.26493/1855-3974.1907.3c2

  189. (with Paul Thomas Young) Convolutions of generalized Stirling numbers and degenerate Bernoulli polynomials, Fibonacci Quart. 58 (2020), 361--366.

  190. (with Leonid G. Fel and Ade Irma Suriyajaya) A sum of negative degrees of the gaps values in 2 and 3-generated numerical semigroups, Ann. Math. Inform. 52 (2020), 85-95. doi:10.33039/ami.2020.08.001

  191. (with Rusen Li), Several identities of classical, complementary and generalized Euler numbers, Filomat 34 (2020), no.10, 3517-3527.

  192. (with Miho Aoki) Remarks on hypergeometric Cauchy numbers,  Math. Rep. (Bucur.) 22 (2020), no.3-4, 363-380. 

  193. (with Gopal Krishna Panda) On several kinds of sums of balancing numbers, Ars Combin. 153 (2020), 127--147.  https://arxiv.org/abs/1608.05918

  194. (with Rusen Li) Infinite series containing generalized $q$-harmonic numbers, Integers 21 (2021),  Paper No. A1, 13 pp.

  195. (with Jagannath Bhanja and Ram Krishna Pandey) Direct and inverse problems for restricted signed sumsets in integers, Contrib. Discrete Math. 26 (2021), 28--46.

  196. (with Kalyan Chakraborty) Generalized hypergeometric Bernoulli numbers, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 115 (2021), Article No.101. 14p. 

  197. (with Ram Krishna Pandey) On hypergeometric Cauchy numbers of higher grade, AIMS Math. 6 (2021), no.7, 6630--6646.

  198. Several continued fraction expansions of generalized Cauchy numbers, Bull. Malays. Math. Sci. Soc. 44 (2021), 2425--2446.  10.1007/s40840-021-01074-2

  199. (with Yuan Zhang) Weighted Sylvester sums on the Frobenius set, Irish Math. Soc. Bull. 87 (2021), 35--43.

  200. (with Jose L. Ramirez and Diego Villamizar) A combinatorial approach to the generalized central factorial numbers, Mediterr. J. Math.  18 (2021), 18 (2021), Article:192, 14 pages. DOI:10.1007/s00009-021-01830-5

  201. (with Leonid G. Fel and Ade Irma Suriyajaya) A sum of negative degrees of the gaps values in two-generated numerical semigroups and identities for the Hurwitz zeta function. In: Nathanson M.B. (eds) Combinatorial and Additive Number Theory IV. CANT 2020. Springer Proceedings in Mathematics & Statistics, vol 347. Springer, Cham., 2021.

  202. (with Jose L. Ramirez and Diego Villamizar) A combinatorial approach to the Stirling numbers of the first kind with higher level, Stud. Sci. Math. Hung. 58 (2021), 293--307.

  203. (with Rusen Li) Summation formulas of $q$-hyperharmonic numbers, Afr. Mat. 32 (2021), 1179--1192.  DOI:10.1007/s13370-021-00891-9

  204. Asymmetric circular graph with Hosoya index and negative continued fractions, Carpathian Math. Publ. 13 (2021), no.3, 608--618.

  205. A parametric type of Cauchy polynomials with higher level, Axioms 10 (2021), No.3, Article:207, 14 pages.   DOI: 10.3390/axioms10030207

  206. (with Narakorn Rompurk Kanasri and Vichian Laohakosol) Cameron's operator in terms of determinants, and hypergeometric numbers, Bol. Soc. Mat. Mex. 28 (2022), Article 9, 23 pp.

  207. Recurrence relations of poly-Cauchy numbers by the r-Stirling transform, Mediterr. J. Math. 19 (2022), No. 1, Paper No. 37, 18 p.

  208. Stirling numbers with level 2 and poly-Bernoulli numbers with level 2, Publ. Math. Debrecen, 100 (2022), 241--261.

  209. (with Yuan Zhang) Weighted Sylvester sums on the Frobenius set in more variables, Kyushu J. Math. 76 (2022), 163--175.   doi:10.2206/kyushujm.76.163 

  210. Sylvester power and weighted sums on the Frobenius set in arithmetic progression, Discrete Appl. Math. 315 (2022), 110--126.  

  211. (with Jose L. Ramirez and Victor F. Sirvent) Some combinatorial identities involving q-harmonic numbers, J. Nonlinear Convex Anal. 23 (2022), no.5, 847-857.

  212. Sylvester sums on the Frobenius set in arithmetic progression, In: F. Yilmaz et al. (eds.), Mathematical Methods for Engineering Applications, Springer Proceedings in Mathematics & Statistics, vol. 384. Springer, Cham., 2022.  pp.1-23. 

  213. (with Eli Bagno and David Garber) A q,r-analogue for the Stirling numbers of the second kind of Coxeter groups of type B, Pure Math. Appl. (PU.M.A.) 30 (2022), no. 1, 8--16.

  214. A parametric type of Bernoulli polynomials with higher level, Res. Math. 30 (2022), No.1, 39--55.

  215. The Frobenius number for sequences of triangular numbers associated with number of solutions, Ann. Comb. 26 (2022) 757-779.

  216. A parametric type of Cauchy polynomials, Miskolc Math. Notes 23 (2022), No.2, 755--772. DOI:10.18514/MMN.2022.3652

  217. Convolution identities of poly-Cauchy numbers with level 2, Rend. Semin. Mat. Univ. Padova 148 (2022), 245-262.  DOI 10.4171/RSMUP/106

  218. (with Haotian Ying) The p-Frobenius and p-Sylvester numbers for Fibonacci and Lucas triplets, Math. Biosci. Eng. 20 (2023), No.2, 3455--3481. doi: 10.3934/mbe.2023162

  219. (with Claudio Pita-Ruiz) The Frobenius number for Jacobsthal triples associated with number of solutions, Axioms 12 (2023), no.2, Article 98, 18 pages.  

  220. The Frobenius number associated with the number of representations for sequences of repunits, Comptes Rendus Mathematique 361 (2023), 73-89.

  221. (with Victor F. Sirvent), Poly-Cauchy numbers with higher level, Symmetry 15 (2023), Article 354, 13 pages.

  222. On s-Stirling transform and poly-Cauchy numbers of the second kind with level 2, Aequationes Math. 97 (2023), 31-61.  DOI:10.1007/s00010-022-00931-0

  223. (with Bijan Patel and Claudio Pita-Ruiz) Several formulas for Bernoulli numbers and polynomials, Adv. Math. Commun. 17 (2023), No.3, 522-535.  

  224. (with Shanta Laishram and Pooja Punyani) p-numerical semigroups of generalized Fibonacci triples, Symmetry 15 (2023), no.4, Article 852, 13 pages. 

  225. Sylvester sums on the Frobenius set in arithmetic progression with initial gaps, In: P. Debnath et al. (eds.), Advances in Number Theory and Applied Analysis, World Scientific (2023), 99-136.    https://doi.org/10.1142/13314  

  226. (with Haotian Ying) The p-numerical semigroup of the triple of arithmetic progressions, Symmetry 15 (2023), no.7, Article 1328, 17 pages.  

  227. (with Rusen Li) Summation formulas of hypergeometric numbers with their generalizations, Afr. Mat. 34 (2023), no.4, Article number 81, 21 p.

  228. (with Vichian Laohakosol) The p-Frobenius problems for the sequence of generalized repunits, Results Math. 79 (2024), no.2, Article No. 26, 25 pages.  doi: 10.1007/s00025-023-02055-6

  229. On the determination of p-Frobenius and related numbers using the p-Apery set, Rev. R. Acad. Cienc. Exactas Fis. Nat., Ser. A Mat., RACSAM 118 (2024), Article 58, 17 pages. 

  230. (with Pin Wang) A generalization of Mneimneh's binomial sum of harmonic numbers, Discrete Math. 347 (2024), No. 5, Article 113945, 6 p.

  231. (with Ruze Yin) p-numerical semigroups of the triples of the sequence (a^n-b^n)/(a-b), V. Gayoso Martinez et al. (eds.), Mathematical Methods for Engineering Applications, Springer Proceedings in Mathematics & Statistics 439, pp.15-29 (Ch. 2), Springer, Cham, 2024. 
    DOI: 10.1007/978-3-031-49218-1_2

  232. (with Haotian Ying) P-Frobenius problem and p-symmetric numerical semigroup, J. Zhejiang Sci-Tech Univ. 51 (2024), no.2, 265--270 (in Chinese).   DOI:10.3969/j.issn.1673-3851(n).2024.02.015

  233. (with Haotian Ying) p-numerical semigroups with p-symmetric properties, J. Algebra Appl. (2024), 2450216 (24 pages). doi: 10.1142/S0219498824502165 

  234. On q-generalized (r,s)-Stirling numbers, Aequationes Math. (online first). doi:10.1007/s00010-023-00997-4 

  235.  (with Khalil Ayadi) Continued fraction expansions towards Zaremba's conjecture, Exp. Math. 33 (2024), (online first).

  236. The Frobenius number for shifted geometric sequences associated with the number of solutions, Publ. Math. Debrecen 105 (2024), No.3-4, (to appear). 

Other papers/Proceedings

  1. Sur le probleme d'approximation diophantinne de Littlewood: une genralisation du theoreme de Baker, , 1992--1993, p1--6.

  2. On inhomogeneous Diophantine approximation and inhomogeneous continued fraction expansion, Surikaisekikenkyushokokyuroku 961 (1996), 125--136

  3. Algebraic independence of some values of certain power series, 5th meeting for transcendental number theory at Gakushuin University, 199745--53 (Japanese).

  4. On an inhomogeneous Diophantine approximation problem of e, Surikaisekikenkyushokokyuroku 1091 (1999), 18--26 (Japanese).

  5. On palindromic sequences from irrational numbers, Talks’ abstracts in Algebra section at the meeting of Mathematical Society of Japan(March 25 to 28, 1999, Gakushuin University), pp.8--11 (Japanese).

  6. Continued fractions and Newton’s approximations, Talks’ abstracts in Algebra section at the meeting of Mathematical Society of Japan(March 27 to 30, 2000,Waseda University), pp.38--39 (Japanese).

  7. On inhomogeneous Diophantine approximation and the Borweins' algorithm, Surikaisekikenkyushokokyuroku 1160 (2000), 155--162 (Japanese).

  8. The number of solutions of Frobenius’s Diophantine equation, Talks’ abstracts in Algebra section at the meeting of Mathematical Society of Japan (March 27 to 31, 2002, Meiji University), pp.16--17 (Japanese).

  9. Continued fractions showing new regularities —Tasoev’s continued fractions, Surikaisekikenkyushokokyuroku 1274 (2002), 100--108 (Japanese).

  10. Arithmetic properties of convergents of e1/s, Talks’ abstracts in Algebra section at the meeting of Mathematical Society of Japan  (September 25 to 28, Shimane University), pp.130--131 (Japanese). 

  11. Arithmetic properties of the leaping convergents of e^(1/s), Surikaisekikenkyushokokyuroku  1319 (2003), 85--94 (Japanese). 

  12. Infinite sum representation algorithm of continued fraction expansions, II, The 5tth Symposium on Algebra and Computation, Tokyo Metropolitan University.

  13. A reverse algorithm of continued fraction expansions, Talks’ abstracts in Algebra section at the meeting of Mathematical Society of Japan(March 28 to 31, 2004, Tsukuba University), pp.10--11 (Japanese).

  14. From continued fractions to real numbers, Surikaisekikenkyushokokyuroku 1384 (2004), 15--23 (Japanese).

  15. Tasoev continued fractions and Rogers-Ramanujan continued fractions, Talks’ abstracts in Algebra section at the meeting of Mathematical Society of Japan(September 19 to 22, 2004, HokkaidoUniversity), pp.142--143 (Japanese).

  16. An algorithm of infinite sums’ representations associated with Tasoev continued fractions, Bunyakovsky International Conference, Abstracts, Kiev (2004), p.164.

  17. The number of solutions on a Frobenius problem, Combinatorial Number Theory and Algebraic Combinatorics, November 18---21, 2002, Yamagata Univ., Eds. By M. Ozeki and E. Bannai, pp. 138—150, 2005.

  18. Rational approximations to Tasoev continued fractions, Surikaisekikenkyushokokyuroku 1511 (2006), 166-172 (Japanese).

  19. (with Carsten Elsner and Iekata Shiokawa) On convergents formed by Pythagorean numbers, Seminar on Mathematical Sciences, No.35, 2006, eds. by M. Katsurada, T. Komatsu and H. Nakada, Keio University, pp. 59--76.

  20. More on the continued fractions of e^2, ,Seminar on Mathematical Sciences, No.35, 2006, eds. by M. Katsurada, T. Komatsu and H. Nakada, Keio University, pp. 111--124.

  21. Approximation to the values of hyperbolic functions by Pythagorean numbers, Talks’ abstracts in Algebra section at the meeting of Mathematical Society of Japan  (September 21 to 24, 2007, Tohoku University), pp.109--110 (Japanese).

  22. Leaping convergents of Hurwitz continued fractions, Diophantine Analysis and related fields (DARF2007/2008), AIP Conf. Proc. 976, Amer. Inst. Phys., Melville, NY, 2008, pp.130--143.

  23. Shrinking the periods of continued fractions, Talks’ abstracts in Algebra section at the meeting of Mathematical Society of Japan 　(March 23 to 26, 2008, Kinki University), pp.31--32 (Japanese).

  24.  Four-term leaping recurrence relations, Talks’ abstracts in Algebra section at the meeting of Mathematical Society of Japan  (September 24 to 27, 2008, Tokyo Institute of Technology, pp.45—46  (Japanese).

  25. Four-term leaping recurrence relations, Surikaisekikenkyushokokyuroku 1639 (2009), 1--11.

  26. Fibonacci-Lucas Zeta functions, Talks’ abstracts in Algebra section at the meeting of Mathematical Society of Japan  (March 26 to 29, 2009,  University of Tokyo), pp.49--50 (Japanese).

  27. Diophantine approximations with leaping convergents, Surikaisekikenkyushokokyuroku 1665 (2009), pp.67--79.

  28. Liouville numbers on non-Archimedean values, Talks’ abstracts in Algebra section at the meeting of Mathematical Society of Japan  (March 24 to 27, Keio University), pp.91—92 (Japanese).

  29.  Some recognizable forms of simple continued fractions, Diophantine Analysis and related fields (DARF2010), AIP Conf. Proc. 1264, Amer. Inst. Phys., Melville, NY, 2010, pp.27--40.

  30. (with H. Belbachir and L. Szalay) Characterization of linear recurrences associated to rays in Pascal's triangle, Diophantine Analysis and related fields (DARF2010), AIP Conf. Proc. 1264, Amer. Inst. Phys., Melville, NY, 2010, pp.90--99.

  31. Linear recurrence relations associated with Pascal triangle, Talks’ abstracts in Algebra section at the meeting of Mathematical Society of Japan  (September 22 to 25, 2010, Nagoya University), pp.62—63  (Japanese).

  32. (with T. Chaichana and V. Laohakosol)Independence of Liouville series, AIP Conf. Proc. 1309, Amer. Inst. Phys., Melville, NY, 2010, pp. 200--205.

  33. On some characteristic properties of linear recurrences associated to rays in Pascal's triangle and combinatorial identities, 　(March 14—15, 2011, Naresuan University, Thailland), p.81.

  34. Linear recurrence relations associated with Generalized Pascal triangles and combinatorial identities, DIMACOS11-FSTM,International Conference on Discrete Mathematics & Computer Sciences　(May 5—8, 2011, University of Hassan II, Mohammedia, Morocco) p.82.

  35. Diophantine approximations of Hurwitz and Tasoev continued fractions,International V. Ya. Skorobohatko Mathematical conference, September 19—23, 2011, Drohobych, Ukraine, Abstracts, p.101.

  36. Arithmetical properties of the leaping convergents of continued fractions, Surikaisekikenkyushokokyuroku  (to appear).

  37. Poly-Cauchy numbers, Surikaisekikenkyushokokyuroku  1806 (2012), 42--53.

  38. (with P. Ruengsinsub, V. Laohakosol and S. Srisopha) Results about dependence and convolution, Surikaisekikenkyushokokyuroku  1806 (2012), 54--64.

  39. Poly-Cauchy numbers and their characteristic properties, International Conference in Number Theory and Applications 2012, Kasetsert University, Bangkok, Thailand, p.34.

  40. Poly-Cauchy polynomials, 8eme Recontre d’Analyse Mathematique et ses Applications (RAMA8) Resumes/Abstracts, Alger, 26—29 Novembre 2012, Faculte de Mathematiques, USTHB, p.14.

  41. (with K. Kamano) Poly-Cauchy polynomials, Talks’ abstracts in Algebra section at the meeting of Mathematical Society of Japan  (March 20 to 23, 2013, Kyoto University), pp.133—134 (Japanese).

  42. Poly-Cauchy numbers and poly-Bernoulli numbers,  Surikaisekikenkyushokokyuroku 1874 (2014), 98--111.

  43. Explicit formulae for sums of products of Bernoulli polynomials, including poly-Bernoulli polynomials, The 8th Fukuoka Number Theory conference. 

  44. A note on the denominators of Bernoulli numbers, Talks’ abstracts in Algebra section at the meeting of Mathematical Society of Japan  (March 15 to 18, Gakushuin  University), p.129 (Japanese).

  45. (with V. Laohakosol, S. Prugsapitak, and J. Rattanamoong)Independence of complex Cantor series and Cantor products, Surikaisekikenkyushokokyuroku 1898 (2014), 47--57.

  46. Convolution identities for Cauchy numbers of the first kind and of the second kind, Surikaisekikenkyushokokyuroku  1898 (2014), 174--193.

  47. A note on the denominators of Bernoulli numbers, Talks’ abstracts in Algebra section at the meeting of Mathematical Society of Japan  (March 15 to 18, 2014, Gakushuin University), pp.129.

  48. Incomplete Stirling numbers, II. Kotet, 2014, 9—12.

  49. Euler numbers and related numbers, and their applications, 10th Fukuoka Number Theory, 2016, #12.  http://auemath.aichi-edu.ac.jp/~ykishi/FSNT/16/012-Komatsu.pdf

  50. Convolution identities for Cauchy numbers of the first kind and of the second kind, Surikaisekikenkyushokokyuroku  2013 (2016), 81--93.

  51. Several generalizations and applications of incomplete poly-Bernoulli polynomials and incomplete poly-Cauchy polynomials, Surikaisekikenkyushokokyuroku  2014 (2017), 174--193.

  52. Several new characteristic properties of Appell polynomials, Automorphic Forms and Related Topics, RIMS Kokyuroku 2055 (2017), 10--23.

  53. Hypergeometric-type Bernoulli-Carlitz, Cauchy-Carlitz and Euler-Carlitz numbers, Proceedings of the 11th Fukuoka Symposium on Number Theory, #12, 105--115.

  54. Fibonacci determinants, Proceedings of the 16th Japan Fibonacci Meeting, held at Tokyo University of Science on August 24, 2018, pp.112--120 (Japanese).

  55. Degenerate Bernoulli polynomials and poly-Cauchy polynomials, RIMS Kokyuroku 2092 (2018), 146–159.

  56. Diophantine Frobenius problems from semigroup's series and identities for zeta functions, RIMS Kokyuroku 2100 (2019), 21–34.

  57. Some approximation properties of hypergeometric Bernoulli numbers, RIMS Kokyuroku 2131 (2019), 84-94.

  58. Topological index associated with continued fractions, Proceedings of the 17th Japan Fibonacci Meeting, held at Tokyo University of Science on August 23, 2019, pp.138–147.

  59. Some generalizations of harmonic numbers and their applications, RIMS Kokyuroku 2162 (2020), 92--103.

  60. Bernoulli and Cauchy numbers with level 2 associated with Stirling numbers with level 2, RIMS Kokyuroku 2222 (2022), 24--38.

  61. Arithmetic approach to p-numerical semigroups, RIMS Kokyuroku 2264 (2023), 1 --16.

  62. The p-Frobenius numbers for Fibonacci triples, Proceedings of the 21st Japan Fibonacci Meeting, held at Tokyo University of Science on August 25, 2023, pp.41--49. 

  63. Diophantine problems of the equations $x^2-y^2=z^r$, RIMS Kokyuroku (to apper). 

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