Yangcheng Li

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 27, 2021, Number 3, Pages 113–118

DOI: 10.7546/nntdm.2021.27.3.113-118

**Full paper (PDF, 199 Kb)**

## Details

### Authors and affiliations

Yangcheng Li

*School of Mathematics and Statistics, Changsha University of Science and Technology,
Changsha, 410114, People’s Republic of China*

### Abstract

It is well known that the number is called the -th -gonal number, where . Many Diophantine equations about polygonal numbers have been studied. By the theory of Pell equation, we show that if is a positive integer but not a perfect square, , and the Diophantine equation

has a nonnegative integer solution , then it has infinitely many positive integer solutions of the form , where and , .

### Keywords

- Polygonal number
- Diophantine equation
- Pell equation
- Positive integer solution

### 2020 Mathematics Subject Classification

- 11D09
- 11D72

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## Cite this paper

Li, Y. (2021). A Diophantine equation about polygonal numbers. *Notes on Number Theory and Discrete Mathematics*, 27(3), 113-118, DOI: 10.7546/nntdm.2021.27.3.113-118.