ELMO SL 2010 N3
Prove that there are infinitely many quadruples of integers such that \begin{align*} a^2 + b^2 + 3 &= 4ab c^2 + d^2 + 3 &= 4cd 4c^3 - 3c &= a \end{align*}
Travis Hance.
Dataset text AI-MO AoPS. Quoted with source.
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