# 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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