Maybe I am wrong. An Counterexample.

来源: 于 2012-03-11 12:04:18 [旧帖] [给我悄悄话] 本文已被阅读：次

Consider the solution of quadratic equation x^2 + 4xy + y^2 = c. x, y are integers iff
3y^2 + c is a square. If c does not have factor 3, or is a square, it is impossible. Easy to find counterexample:

x = 13 (1, 2), y = 22 (1, 3) and x^2 + 4xy + y^2 = 286 has no interger solution.