On The Jésmanowicz Conjecture Of Pythagorean Triples

In this paper,we prove that the conjecture of Je(?)manowicz concerning pythagore-an triples for the diophantine equation(n2-4)x +(4n)y =(n2 + 4)z holds in a special case.Base on the method of algebraic number theory,recursion sequence method and quadratic residue.we get the following results:Theorem 1 Assuming that n = ps(p is a prime number,s belongs to s ? Z+),so the conjecture of Je(?)manowicz for the diophantine equation(n2-4)x +(4n)y =(n2 + 4)z holds when n ?-1(mod 16).Theorem 2 Assuming that n2 + 4 =ps(p is a prime number,s belongs to s ? Z+),so the conjecture of Je(?)manowicz for the diophantine equation(n2-4)x +(4n)y =(n2+4)z holds when n ?-1(mod 16).