MathDB

f(n+p) != f(n) for any n and prime p

Source: Balkan MO 2010, Problem 4

May 4, 2010

functionnumber theorygreatest common divisorrelatively primetotient functionnumber theory proposed

Problem Statement

For each integer

n

(

n \ge 2

), let

f(n)

denote the sum of all positive integers that are at most

n

and not relatively prime to

n

. Prove that

f(n+p) \neq f(n)

for each such

n

and every prime

p