On Jesmanowicz' conjecture concerning Pythagorean numbers

Let a, b be positive integers such that ab, gcd (a, b) - 1 and 2|ab, then it can be proved that if 2||ab, the equation (a2 - b2)x + (2ab)y = (a2 + b2)z has only the positive integer solution (x, y, z) = (2, 2, 2) with x=y=z=0(mod2).