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 \( 0 .\)

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