Question 125
a. Let $a$ and $b$ be positive integers so $M(a, b) = a - \frac{1}{b} + b \left(b + \frac{3}{a}\right)$ is an integer. Prove that $M(a, b)$ is a square.
b. Find integers $a$ and $b$, both unequal to zero, so $M(a, b)$ is a positive integer, but not square.
b. Find integers $a$ and $b$, both unequal to zero, so $M(a, b)$ is a positive integer, but not square.