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beautiful number theory inequality

Source: 239 Open MO, 2018, Junior League, Problem 6

April 4, 2023
number theoryinequalities

Problem Statement

Petya wrote down 100 positive integers n,n+1,…,n+99n, n+1, \ldots, n+99, and Vasya wrote down 99 positive integers m,m−1,…,m−98m, m-1, \ldots, m-98. It turned out that for each of Petya's numbers, there is a number from Vasya that divides it. Prove that m>n3/10,000,000m>n^3/10, 000, 000. Proposed by Ilya Bogdanov
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