Problem 3

(Problem Posed by Department of Mathematics, Sarada Vilas College, Mysuru)

Suppose \(φ(n)\) represents the Euler's Totient function, that is number of positive integers less than \(n\) which are relatively prime with \(n\). Find at least one natural number \(n\) such that

\(n = φ(n)+10\),

if it exists. If there exists no such \(n\), prove the same. You can either comment your solution below or send the same to dep.math.svc@gmail.com on or within 12th of October 2022.

Note. Two natural numbers \(a\) and \(b\) are said to be relatively prime if they do not have any common factors other than 1.