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What is the largest integer n≤1000 n \leq 1000 n≤1000, such that there exist 2 non-negative integers (a,b)(a, b)(a,b) satisfying
n=a2+b2ab−1? n = \frac{ a^2 + b^2 } { ab - 1 } ? n=ab−1a2+b2?
Hint: (a,b)=(0,0) (a,b) = (0,0) (a,b)=(0,0) gives us 02+020×0−1=0 \frac{ 0^2 + 0^2 } { 0 \times 0 - 1 } = 00×0−102+02=0, so the answer is at least 0. 0 .0.
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