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diophantine (x + y + z)^5 = 80xyz(x^2 + y^2 + z^2)

Source: Balkan BMO Shortlist 2016 N3

July 30, 2019
number theoryDiophantine equationdiophantineIMO Shortlist

Problem Statement

Find all the integer solutions (x,y,z)(x,y,z) of the equation (x+y+z)5=80xyz(x2+y2+z2)(x + y + z)^5 = 80xyz(x^2 + y^2 + z^2),
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