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x^2 + y + z^2 = nxyz in positive integers

Source: Estonia IMO TST 2014 p6

April 5, 2020
diophantineDiophantine equationnumber theory

Problem Statement

Find all natural numbers nn such that the equation x2+y2+z2=nxyzx^2 + y^2 + z^2 = nxyz has solutions in positive integers
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