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 (n2 - 4)x+(4n)y= (n2+4)z holds in a special case n≡ - 1(mod 16). Base on the method of algebraic number theo-ry, comparative method of prime factors,recursion sequence method and quadratic residue.Theorem 1.Assuming that n2+4 is a prime number,for the diophantine equation (n2-4)x+(4n)y= (n2+4)z the conjecture of Jesmanowicz holds.Theorem 2.Assuming that n is an odd prime number,for the diophantine equation (n2-4)x+(4n)y=(n2+4)z the conjecture of Jesmanowicz holds.