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Fifth and sitxh power of prime

Source: 2021 Nigerian MO Round 3/P3

December 19, 2022
Diophantine equationnumber theoryprime

Problem Statement

Find all pairs of natural numbers (p,n)(p, n) with pp prime such that p6+p5+n3+n=n5+n2p^6+p^5+n^3+n=n^5+n^2.
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