Question 37
A pair of polynomials $F(x, y)$, $G(x, y)$ with integer coefficients is called *important*, if the following condition holds: if for some integers $a, b, c, d$ both $F(a, b) - F(c, d)$ and $G(a, b) - G(c, d)$ are divisible by 100, then both $a - c$ and $b - d$ are divisible by 100. Determine if there exist an important pair of polynomials $P(x, y)$, $Q(x, y)$ such that the pair $P(x, y) - xy$, $Q(x, y) + xy$ is also important.