Given an integer k>1, show that there exist an integer an n>1 and distinct positive integers a1,a2,⋯an, all greater than 1, such that the sums ∑j=1naj and ∑j=1nϕ(aj) are both k-th powers of some integers.
(Here ϕ(m) denotes the number of positive integers less than m and relatively prime to m.) number theoryrelatively primenumber theory unsolved