MathDB

3

Part of 2021 Azerbaijan IZhO TST

Problems(1)

good qstn

Source:

10/21/2010
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.
number theoryrelatively primenumber theory unsolved