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min a such that (a^p -a)/ p =b^2

Source: 2022 Saudi Arabia JBMO TST 1.4

November 3, 2022
number theoryPerfect Square

Problem Statement

Determine the smallest positive integer aa for which there exist a prime number pp and a positive integer b≥2b \ge 2 such that ap−ap=b2.\frac{a^p -a}{p}=b^2.
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