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system in integers, a^2+b^2=5mn and m^2+n^2=5ab

Source: Rioplatense Olympiad 2001 level 3 P1

September 6, 2018
system of equationsnumber theory

Problem Statement

Find all integer numbers a,b,ma, b, m and nn, such that the following two equalities are verified: a2+b2=5mna^2+b^2=5mn and m2+n2=5abm^2+n^2=5ab
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