Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 3, Pages 113—118
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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 , .
- Polygonal number
- Diophantine equation
- Pell equation
- Positive integer solution
2020 Mathematics Subject Classification
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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.