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2011 Japan Mathematical Olympiad Finals Problem 2

Source: Japanese MO Finals 2011

February 11, 2011
number theory proposednumber theoryZsigmondy

Problem Statement

Find all of quintuple of positive integers (a,n,p,q,r)(a,n,p,q,r) such that an−1=(ap−1)(aq−1)(ar−1)a^n-1=(a^p-1)(a^q-1)(a^r-1) .
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