JEŚMANOWICZ’ CONJECTURE REVISITED

Let a, b, cbe relatively prime positive integers such that {a}^{2} + {b}^{2} = {c}^{2} . In 1956, Jeśmanowicz conjectured that for any positive integer n, the only solution of \mathop{(an)}\nolimits ^{x} + \mathop{(bn)}\nolimits ^{y} = \mathop{(cn)}\nolimits ^{z} in positive integers is (x, y, z)= (2, 2, 2). In this paper, we consider Jeśmanowicz’ conjecture for Pythagorean triples (a, b, c)if a= c- 2and cis a Fermat...