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

A conjecture proposed by Jeśmanowicz on Pythagorean triples states that for any fixed primitive Pythagorean triple (a,b,c) such that a2+b2=c2, the Diophantine equation ax+by=cz 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.