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pro vyhledávání: '"Ray, Prasanta Kumar"'
Autor:
Bhoi, Kisan, Ray, Prasanta Kumar
Padovan sequence is a ternary recurrent sequence defined by the recurrence relation $P_{n+3}=P_{n+1}+P_{n}$ with initial terms $P_{0}=P_{1}=P_{2}=1.$ In this study it is shown that $114,151,200,265,351,465,616,816,3329,4410,7739,922111$ are the only
Externí odkaz:
http://arxiv.org/abs/2212.10831
Autor:
Bhoi, Kisan, Ray, Prasanta Kumar
Publikováno v:
Communications in Mathematics, Volume 31 (2023), Issue 1 (December 22, 2022) cm:10476
In this study we find all solutions of the Diophantine equation $B_{n_{1}}+B_{n_{2}}=2^{a_{1}}+2^{a_{2}}+2^{a_{3}}$ in positive integer variables $(n_{1},n_{2},a_{1},a_{2},a_{3}),$ where $B_{n}$ denotes the $n$-th balancing number.
Comment: 18 p
Comment: 18 p
Externí odkaz:
http://arxiv.org/abs/2212.06372
In this study, we find all Pell and Pell-Lucas numbers which are sums of three base 10 repdigits. The proof of our main theorem uses lower bounds for linear forms in logarithms of algebraic numbers and a version of the Baker-Davenport reduction metho
Externí odkaz:
http://arxiv.org/abs/2009.12607
Autor:
Behera, Mitashree, Ray, Prasanta Kumar
Publikováno v:
International Journal of Number Theory; Nov2024, Vol. 20 Issue 10, p2491-2507, 17p
Autor:
Behera Adikanda, Ray Prasanta Kumar
Publikováno v:
Acta Universitatis Sapientiae: Mathematica, Vol 13, Iss 2, Pp 305-320 (2021)
In this note the convolved (u, v)-Lucas first kind and the convolved (u, v)-Lucas second kind p-polynomials are introduced and study some of their properties. Several identities related to the common generalization of convolved (u, v)-Lucas first and
Externí odkaz:
https://doaj.org/article/c659d2894ec3415daa54f074d68635ff
Autor:
Komatsu, Takao, Ray, Prasanta Kumar
Let $B_n$ be the $n$-th balancing number. In this paper, we give some explicit expressions of $\sum_{l=0}^{2 r-3}(-1)^l\binom{2 r-3}{l}\sum_{j_1+\cdots+j_r=n-2 l\atop j_1,\dots,j_r\ge 1}B_{j_1}\cdots B_{j_r}$ and $\sum_{j_1+\cdots+j_r=n\atop j_1,\dot
Externí odkaz:
http://arxiv.org/abs/1608.05925
Publikováno v:
Discussiones Mathematicae - General Algebra and Applications, Vol 40, Iss 2, Pp 201-216 (2020)
In this note, the finite alternating sums of reciprocals of balancing and Lucas-balancing numbers are considered and several identities involving these sums are deduced.
Externí odkaz:
https://doaj.org/article/9e7944f44940413994fd0e01177565f1
Publikováno v:
Discussiones Mathematicae - General Algebra and Applications, Vol 40, Iss 1, Pp 37-48 (2020)
In this note we study the analytic continuation of the Apostol-Vu multiple Fibonacci zeta functions ζAVF,k(s1,…,sk,sk+1)=∑1≤m1
Externí odkaz:
https://doaj.org/article/30ea2966383e4858b6f4fbbd74f1c088
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Autor:
Ray, Prasanta Kumar
Publikováno v:
In Ain Shams Engineering Journal September 2018 9(3):395-402