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