Diophantine equations related to reciprocals of linear recurrence sequences

H. R. Hashim and Sz. Tengely
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 2, Pages 49-56
DOI: 10.7546/nntdm.2019.25.2.49-56
Full paper (PDF, 195 Kb)

Details

Authors and affiliations

H. R. Hashim
Mathematical Institute, University of Debrecen
P. O. Box 12, 4010 Debrecen, Hungary

Sz. Tengely
Mathematical Institute, University of Debrecen
P. O. Box 12, 4010 Debrecen, Hungary

Abstract

In the past years, many researchers have worked on degenerate polynomials and a variety of its extentions and variants can be found in literature. Following up, in this article, we firstly introduce the partially degenerate Legendre–Genocchi polynomials, and further define a new generalization of degenerate Legendre–Genocchi polynomials. From our generalization, we establish some implicit summation formulae and symmetry identities by the generating function of partially degenerate Legendre–Genocchi polynomials. Eventually, it can be found that some recently demonstrated summations and identities stated in the article, are special cases of our results.

Keywords

• Recurrence sequences
• Diophantine equations

2010 Mathematics Subject Classification

• 11D25
• 11B39

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