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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