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An old NT problem

Source: 2023 Taiwan Mathematics Olympiad

February 8, 2023
Taiwan

Problem Statement

Find all positive integers nn satisfying the following conditions simultaneously:
(a) the number of positive divisors of nn is not a multiple of 88; (b) for all integers xx, we have xn≡xmod  n.x^n \equiv x \mod n.
Proposed by usjl
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