# What is $$m^2+n^2$$?

Determine the maximum value of $$m^2 + n^2$$, where $$m$$ and $$n$$ are integers satisfying $$m, n \in \{ 1,2, \ldots , 1981 \}$$ and $$( n^2 - mn - m^2 )^2 = 1$$.

Source: IMO 1981.

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