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On values of (1-p^m)^n+(1-q^n)^m

Source: Poland Math Olympiad 1993 Round 1 #10

June 4, 2023
inequalities

Problem Statement

Given positive real numbers p,qp,q with p+q=1p+q=1. Prove that for all positive integers m,nm,n the following inequality holds (1−pm)n+(1−qn)m≥1(1-p^m)^n+(1-q^n)^m \geq 1.
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