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Large primes powers does not make square

Source: 2024 IMOC N1 (Quiz P1)

August 8, 2024
number theoryprimePerfect Squares

Problem Statement

Proof that for every primes pp, qq pq2−q+1+qp2−p+1−p−qp^{q^2-q+1}+q^{p^2-p+1}-p-q is never a perfect square. Proposed by chengbilly
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