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

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## 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 sequences0
- Diophantine equations.

### 2010 Mathematics Subject Classification

- 11D25
- 11B39

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## Cite this paper

APAHashim, H. R. & Tengely, Sz. (2019). Diophantine equations related to reciprocals of linear recurrence sequences. Notes on Number Theory and Discrete Mathematics, 25(2), 49-56, doi: 10.7546/nntdm.2019.25.2.49-56.

ChicagoHashim, H. R. and Sz. Tengely “Diophantine equations related to reciprocals of linear recurrence sequences.” Notes on Number Theory and Discrete Mathematics 25, no. 2 (2019): 49-56, doi: 10.7546/nntdm.2019.25.2.49-56.

MLAHashim, H. R. and Sz. Tengely. “Diophantine equations related to reciprocals of linear recurrence sequences.” Notes on Number Theory and Discrete Mathematics 25.2 (2019): 49-56. Print, doi: 10.7546/nntdm.2019.25.2.49-56.