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\alpha^{3pq} -\alpha \equiv 0 \pmod {3pq}

Source: Romanian IMO Team Selection Test TST 1996, problem 11

September 27, 2005
modular arithmeticfunctionnumber theory proposednumber theory

Problem Statement

Find all primes p,q p,q such that α3pq−α≡0(mod3pq) \alpha^{3pq} -\alpha \equiv 0 \pmod {3pq} for all integers α \alpha .
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