Question 7
Some integers from 1 through n are red. Whenever red a,b,c (not necessarily distinct) satisfy $n\mid a(b-c)$, one has b=c. Prove that at most $\varphi(n)$ integers are red, where $\varphi(n)$ counts positive integers at most n coprime to n. The official definition uses “at most n”; the book says “less than n”, which differs at n=1.