Question 52
a. Let $a$, $b$, and $n$ be positive integers such that $a b = n^{2} + 1$. Prove that
$$
|a-b| \geq \sqrt{4 n - 3}
$$
b. Prove that there are infinitely many such triples $(a, b, n)$ such that equality occurs.
$$
|a-b| \geq \sqrt{4 n - 3}
$$
b. Prove that there are infinitely many such triples $(a, b, n)$ such that equality occurs.