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 \( 0 .\)
by
Calvin Lin
