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min xyz if x|(y^5+1),y|(z^5+1),z|(x^5+1)

Source: China Northern MO 2015 grade 10 p7 CNMO

May 5, 2024
number theory

Problem Statement

It is known that odd prime numbers x,yzx, y z satisfy x∣(y5+1),y∣(z5+1),z∣(x5+1).x|(y^5+1),y|(z^5+1),z|(x^5+1). Find the minimum value of the product xyzxyz.
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