Define funcitons F, G and H:
F(x,y) = x² - 2xy + y² - 5x + 7y
G(x,y) = x² - 3xy + 2y² + x - y
H(x,y) = xy - 12x + 15y

If x and y are integers and p is an odd prime such that the values of F(x,y) and G(x,y) are both divisible by p, then prove that H(x,y) is also divisible by p.

Seventeen divides expression? is a specific instance of this puzzle where p=17.