On The Je(?)manowicz Conjecture Of Pythagorean Triples

In this paper, we prove that the conjecture of Jesmanowicz concerning pythagore-an triples for the diophantine equation (s2-t2)x+(2st)y = (s2 + t2)z holds true in a special cases. Base on elementary congruence, factorization method, quadratic residue, bi-quadratic residue characters.Theorem.For the case of s-t = m,t = m, (m,n) = 1, if m = 3,5(mod 8) and m exists a factor p such that p = 3(mod 8), the conjecture of Jesmanowicz holds when 2n+m exists a prime factor p such that p≠1 (mod 4).