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n divides x^n-y^n implies n^2 does?

Source: Own. IMO 2022 Malaysian Training Camp 3

April 17, 2022
number theory

Problem Statement

Find all positive integer nn such that for all positive integers x x , y y , n∣xn−yn⇒n2∣xn−yn n \mid x^n-y^n \Rightarrow n^2 \mid x^n-y^n .
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