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n(n+1)(n+2)=m^r, no solutions

Source: VTRMC 2014 P5

May 10, 2021
Diophantine equationnumber theory

Problem Statement

Let n≥1n\ge1 and r≥2r\ge2 be positive integers. Prove that there is no integer mm such that n(n+1)(n+2)=mrn(n+1)(n+2)=m^r.
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