Problem

Show that if x is a nontrivial square root of 1 modulo N, that is, if x2 ≡ 1 mod N but mo...

Show that if x is a nontrivial square root of 1 modulo N, that is, if x2 ≡ 1 mod N but mod N, then N must be composite. (For instance, 42 ≡ 1 mod 15 but 4 mod 15; thus 4 is a nontrivial square root of 1 modulo 15.)

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