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p+q+r >= 20 (VI Soros Olympiad 1990-00 R1 8.1)

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May 27, 2024
number theoryinequalities

Problem Statement

Let p,q,rp,q,r be prime numbers such that 2p>q2p>q, q>2rq > 2r and q>p+rq>p+r. Prove that p+q+r≥20p+q+r\ge 20.
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