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 $m^2+n^2$?
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 $m^2+n^2$?