Past exam of the mathematics course of the University of Cambridge / 2020 / ia / Paper 2 / 7D / a / Solution

The Euler totient function $\varphi (n)$ is the number of residue classes modulo $n$ that are coprime to $n$. The Chinese remainder theorem says that for pairwise coprime moduli $m_i$, reduction induces a bijectionIt restricts to a bijection of unit groups. If $n=p_1\cdots p_r$ is squarefree, thenEach of the primes $3,5,17,257$ is one more than a power of two, so every squarefree product of them has power-of-two totient. Ten odd examples are