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St. Petersburg MO 2017 Grade 11 P4

Source: St. Petersburg MO 2017 Grade 11 P4

May 3, 2018
number theory

Problem Statement

A positive integer nn is called almost-square if nn can be represented as n=abn=ab where a,ba,b are positive integers that a≤b≤1.01aa\leq b\leq 1.01a. Prove that there exists infinitely many positive integers mm that there’re no almost-square positive integer among m,m+1,…,m+198m,m+1,…,m+198.
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