Publication date: 30 June 2023
Volume: Vol 58
Issue: Svezak 1
Pages: 59-65
DOI: 10.3336/gm.58.1.04
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
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 \(y \lt r-1\).
Binary quadratic forms, quadratic diophantine equation, Dujella's conjecture
304390
20.6.2023.
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