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n divides k^k-1 implies n divides k-1

Source: KoMaL A. 843

February 11, 2023
number theorykomal

Problem Statement

Let NN be the set of those positive integers nn for which n∣kk−1n\mid k^k-1 implies n∣k−1n\mid k-1 for every positive integer kk. Prove that if n1,n2∈Nn_1,n_2\in N, then their greatest common divisor is also in NN.
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