Question 76
Find all positive integers $a$ and $b$ such that
$$
(a^2 + b) \mid (a^2b + a) \quad \text{and} \quad (b^2 - a) \mid (ab^2 + b).
$$
$$
(a^2 + b) \mid (a^2b + a) \quad \text{and} \quad (b^2 - a) \mid (ab^2 + b).
$$
MathNet 2013 Question 76
Math Olympiad Vault · MathNet 2013