RIOPLATENSE 2001 Problem 1

Find all integer numbers $a, b, m$ and $n$ , such that the following two equalities are verified: $a^2+b^2=5mn$ and $m^2+n^2=5ab$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.