One solution may lead to another one.

Determine the maximum value of \(m^{2}+n^{2}\), where \(m\) and \(n\) are integers satisfying

i. \(m,n\in \{1,2,....,1981\}\)

ii. \((n^{2}-mn-m^{2})^{2}=1\).

This is an old IMO problem.

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