MathDB
Quantity phi(n)

Source: ToT 2019

December 25, 2019
number theorycombinatorics

Problem Statement

We color some positive integers (1,2,...,n)(1,2,...,n) with color red, such that any triple of red numbers (a,b,c)(a,b,c)(not necessarily distincts) if a(bc)a(b-c) is multiple of nn then b=cb=c. Prove that the quantity of red numbers is less than or equal to φ(n)\varphi(n).