MathNet 1999 — Part 01 Question 27

Let $m$ be a positive integer such that $m \equiv 2 \pmod{4}$. Show that there exists at most one factorization $m = a b$ where $a$ and $b$ are positive integers satisfying $0 \lt a - b \lt \sqrt{5 + 4 \sqrt{4 m + 1}}$.