olymmath

INMO 2019 Problem 3

    Let m,nm, n be distinct positive integers. Prove that

    gcd⁡(m,n)+gcd⁡(m+1,n+1)+gcd⁡(m+2,n+2)≤2∣m−n∣+1\operatorname{gcd}(m, n)+\operatorname{gcd}(m+1, n+1)+\operatorname{gcd}(m+2, n+2) \leq 2|m-n|+1

    Further, determine when equality holds.

    Dataset text NuminaMath olympiads. Quoted with source.

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