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m^2-5n^2 and m^2+5n^2 are both perfect squares

Source: 2020 Korea National Olympiad P4

November 21, 2020
number theoryDiophantine equation

Problem Statement

Find a pair of coprime positive integers (m,n)(m,n) other than (41,12)(41,12) such that m2āˆ’5n2m^2-5n^2 and m2+5n2m^2+5n^2 are both perfect squares.
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