Past exam of the short options course of the University of Oxford / 2017 / 1 / c / Solution

Euler's totient function counts the integers in a complete complete residue system that are coprime to the modulus:If the prime factorization is $n={\prod }_{j=1}^r{p}_j^{e_j}$ with distinct prime numbers $p_j$, Euler's totient product formula isIn particular, $\varphi (2017)=2016$. Adjoining the prime factor $2$ changes neither the odd factor nor its count of units, since $\varphi (2)=1$. The product formula givesThis is a positive integer distinct from $2017$, as required.