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Arithmetic mean of the integers less than and coprime with n

Source: India ISI B.Math Entrance Exam 2006

June 17, 2012
number theory proposed

Problem Statement

Let SS be the set of all integers kk, 1≤k≤n1\leq k\leq n, such that gcd⁡(k,n)=1\gcd(k,n)=1. What is the arithmetic mean of the integers in SS?
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