Maybe I am wrong. An Counterexample.

回答: 有没有好办法？ 由 cma 于 2012-03-10 19:31:33

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.