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October 21, 2010
number theoryrelatively primenumber theory unsolved

Problem Statement

For each n∈Nn \in N let S(n)S(n) be the sum of all numbers in the set {1,2,3,…,n} which are relatively prime to nn. a. Show that 2S(n)2S(n) is not aperfect square for any nn. b. Given positive integers m,nm,n with odd n, show that the equation 2S(x)=yn2S(x)=y^n has at least one solution (x,y)(x,y) among positive integers such that m∣xm|x.
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