MathDB

Problem 5

Part of 2014 VTRMC

Problems(1)

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

Source: VTRMC 2014 P5

5/10/2021
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.
Diophantine equationnumber theory