Question 40
Let $a$ and $b$ be positive integers such that
$$
\frac{a^4-1}{b+1} + \frac{b^4-1}{a+1}
$$
is integer. Prove that $a^{2010}b^{2012} - 1$ is divisible by $a+1$.
$$
\frac{a^4-1}{b+1} + \frac{b^4-1}{a+1}
$$
is integer. Prove that $a^{2010}b^{2012} - 1$ is divisible by $a+1$.