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FLT fraction is a square

Source: Austrian-Polish 2005, Problem 4

July 5, 2015
fermat's little theoremPerfect Squaresprimenumber theoryDiophantine equation

Problem Statement

Determine the smallest natural number a≥2a\geq 2 for which there exists a prime number pp and a natural number b≥2b\geq 2 such that ap−ap=b2.\frac{a^p - a}{p}=b^2.
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