Question 174
a. Prove: if $a - \frac{1}{b} + b\left(b + \frac{3}{a}\right)$ is an integer for some positive integers $a$ and $b$, then it is a perfect square.
b. Find two integers $a$ and $b$ such that $a - \frac{1}{b} + b\left(b + \frac{3}{a}\right)$ is a positive integer but not a perfect square.
b. Find two integers $a$ and $b$ such that $a - \frac{1}{b} + b\left(b + \frac{3}{a}\right)$ is a positive integer but not a perfect square.