This doesn't seem too likely

Algebra Level 4

What is the largest integer $n \leq 1000$ , such that there exist 2 non-negative integers $(a, b)$ satisfying

$n = \frac{ a^2 + b^2 } { ab - 1 } ?$

Hint: $(a,b) = (0,0)$ gives us $\frac{ 0^2 + 0^2 } { 0 \times 0 - 1 } = 0$ , so the answer is at least $0 .$