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Maximize n over phi n

Source: Canada Repêchage 2017/2

April 13, 2017
number theory

Problem Statement

For any positive integer n, let φ(n)\varphi(n) be the number of integers in the set {1,2,…,n}\{1, 2, \ldots , n\} whose greatest common divisor with nn is 1. Determine the maximum value of nφ(n)\frac{n}{\varphi(n)} for nn in the set {2,…,1000}\{2, \ldots, 1000\} and all values of nn for which this maximum is attained.
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