Original scientific paper

https://doi.org/10.3336/gm.58.1.04

A note on Dujella's unicity conjecture

Maohua Le ; Institute of Mathematics, Lingnan Normal College, Zhangjiang, Guangdong, 524048, China
Anitha Srinivasan ; Departamento de métodos cuantitativos, Universidad Pontificia de Comillas (ICADE), C/ Alberto Aguilera, 23 - 28015, Madrid, Spain

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Abstract

Using properties of binary quadratic Diophantine equations, we prove that if \(r=p^{m} q^{n}\), where \(p, q\) are distinct odd primes and \(m, n\) are positive integers, then the equation \(x^{2}-\left(r^{2}+1\right) y^{2}=r^{2}\) has at most one positive integer solution \((x, y)\) with \(y \lt r-1\).

Keywords

Binary quadratic forms, quadratic diophantine equation, Dujella's conjecture

Hrčak ID:

304390

URI

https://hrcak.srce.hr/304390

Publication date:

20.6.2023.

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