Question 5
Let $a,b$ be positive odd integers satisfying $b\mid a^2+2$ and $a\mid b^2+2$.
a) Prove $ab\mid a^2+b^2+2$.
b) Prove that $\dfrac{a^2+b^2+2}{ab}$ is a perfect square.
a) Prove $ab\mid a^2+b^2+2$.
b) Prove that $\dfrac{a^2+b^2+2}{ab}$ is a perfect square.