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Number Theory

Source: 2004 National High School Mathematics League, Exam Two, Problem 3

March 18, 2020
number theory

Problem Statement

For integer n≥4n\geq4, find the smallest integer f(n)f(n), such that for any positive integer mm, in any subset with f(n)f(n) elements of the set {m,m+1,⋯ ,m+n−1}\{m, m+1, \cdots, m+n-1\} there are at least three elements that are relatively prime .
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