Let $m$ and $n$ be positive integers less than $2000$ which satisfies the equation $(m^2-mn-n^2)^2=1$. How can we determine the largest possible value of the expression $m^2+n^2$?
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2$\begingroup$ Brute force on a computer. This (maybe) belongs to Math Stack Exchange. $\endgroup$– JP McCarthyCommented Apr 18, 2023 at 5:55
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$\begingroup$ artofproblemsolving.com/community/c3046h1048219 $\endgroup$– individCommented Apr 18, 2023 at 7:16
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1$\begingroup$ Why would one want to do this? What's special about $2000$? $\endgroup$– Gerry MyersonCommented Apr 18, 2023 at 7:36
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This is a variant of IMO 1981/3 and can be solved by the exact same method.