find n
Source: Indonesia IMO 2007 TST, Stage 2, Test 2, Problem 2
November 15, 2009
algebra proposedalgebra
Problem Statement
Let be non-zero real numbers satisfying \dfrac{1}{a}\plus{}\dfrac{1}{b}\plus{}\dfrac{1}{c}\equal{}\dfrac{1}{a\plus{}b\plus{}c}. Find all integers such that \dfrac{1}{a^n}\plus{}\dfrac{1}{b^n}\plus{}\dfrac{1}{c^n}\equal{}\dfrac{1}{a^n\plus{}b^n\plus{}c^n}.