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Original paper

A note on Jeśmanowicz’ conjecture for non-primitive Pythagorean triples

Volume: 5, Issue: 1, Pages: 115 - 127
Published: Mar 21, 2021
Abstract
Let \((a, b, c)\) be a primitive Pythagorean triple parameterized as \(a=u^2-v^2, b=2uv, c=u^2+v^2\), where \(u>v>0\) are co-prime and not of the same parity. In 1956, L. Jesmanowicz conjectured that for any positive integer \(n\), the Diophantine equation \((an)^x+(bn)^y=(cn)^z\) has only the positive integer solution \((x,y,z)=(2,2,2)\). In this connection we call a positive integer solution \((x,y,z)\ne (2,2,2)\) with \(n>1\)...
Paper Details
Title
A note on Jeśmanowicz’ conjecture for non-primitive Pythagorean triples
Published Date
Mar 21, 2021
Volume
5
Issue
1
Pages
115 - 127
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