Generalizations of classical results on Jeśmanowicz' conjecture concerning Pythagorean triples II

By T. Miyazaki, Pingzhi Yuan, Danyao Wu. 2013

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Abstract A conjecture proposed by Jeśmanowicz on Pythagorean triples states that for any fixed primitive Pythagorean triple ( a , b , c ) such that a 2 + b 2 = c 2 , the Diophantine equation a x + b y = c z has only the trivial solution in positive integers x , y and z. In this paper we establish the conjecture for the case where b is even and either a or c is congruent to ±1 modulo the product of all prime factors of b.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4d8440c8a2d84f428742b0d953bc298052b6c1d1