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1/(p^n+q^n+1) + 1/(q^n+r^n+1)+ 1/(r^n+p^n+ 1) <=1 if pqr=1

Source: Mathcenter Contest / Oly - Thai Forum 2008 R3 p4 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 9, 2022
algebrainequalities

Problem Statement

Let p,q,r∈R+p,q,r \in \mathbb{R}^+ and for every n∈Nn \in \mathbb{N} where pqr=1pqr=1 , denote 1pn+qn+1+1qn+rn+1+1rn+pn+1≤1 \frac{1}{p^n+q^n+1} + \frac{1}{q^n+r^n+1} + \frac{1}{r^n+p^n+ 1} \leq 1
(Art-Ninja)
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