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A nice joke

Source: Baltic Way 2004 Problem 3

November 19, 2004
inequalitiesinequalities proposed

Problem Statement

Let p,q,rp, q, r be positive real numbers and nn a natural number. Show that if pqr=1pqr = 1, then 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.
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