So $d$ must be a divisor of 1000. Also, both $a$ and $b$ must be divisible by a perfect square greater than 1. Since $a = dx$ and $b = dy$, both $dx$ and $dy$ must be divisible by a square $s > 1$. That means $d$ must contain all the square factors of $s$, or at least $x$ and $y$ must together contain the square factors. - Appfinity Technologies