MathDB

Sum of numbers less than x and coprime to x

Source: 2007 Bulgarian Autumn Math Competition, Problem 10.3

March 17, 2022

number theorycoprimesum function

Problem Statement

For a natural number

m>1

we'll denote with

f(m)

the sum of all natural numbers less than

m

, which are also coprime to

m

. Find all natural numbers

n

, such that there exist natural numbers

k

and

\ell

which satisfy

f(n^{k})=n^{\ell}