This doesn't seem too likely

Algebra Level 4

What is the largest integer n1000 n \leq 1000 , such that there exist 2 non-negative integers (a,b)(a, b) satisfying

n=a2+b2ab1? n = \frac{ a^2 + b^2 } { ab - 1 } ?

Hint: (a,b)=(0,0) (a,b) = (0,0) gives us 02+020×01=0 \frac{ 0^2 + 0^2 } { 0 \times 0 - 1 } = 0, so the answer is at least 0. 0 .

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