An application of Baker’s method to the Jeśmanowicz’ conjecture on primitive Pythagorean triples

Let m, n be positive integers such that $m>n, \gcd (m,n)=1 and m \not \equiv n \pmod {2}. In 1956, L. Jeśmanowicz conjectured that the equation (m^2 - n^2)^x + (2mn)^y = (m^2+n^2)^z has only the positive integer solution (x,y,z) = (2,2,2). This conjecture is still unsolved. In this paper, combining a lower bound for linear forms in two logarithms due to M. Laurent with some elementary methods, we prove that if mn \equiv 2...