Let $a$ and $b$ be two integers. Prove that if $ab=4$, then $(a-b)^3-9(a-b)=0$.

Question

Let $a$ and $b$ be two integers. Prove that if $ab=4$, then $(a-b)^3-9(a-b)=0$.

I have tried to approach this by proving the contrapositive instead, but I'm not sure if that's the best approach to this.

Answer 1

Hint: What are the integer solutions of $ab=4$ ?

Answer 2

Hint: What values can $a$ and $b$ take? Why don't you substitute them into the lhs?