Find all $n$ such that $\varphi(n) \equiv 2 \pmod 4$

Question

My question is

Find all $n$ such that $\varphi(n) \equiv 2 \pmod 4$, where $\varphi(n)$ is the Euler totient function.

I am no where to start so any hint or help ? and if we are given such a problem how can we start

Answer 1

Consider the exhaustive cases:

$n$ is a multiple of two odd primes;

$n$ is an odd prime;

$n$ is twice an odd prime;

$n$ is the product of an odd prime and a power of $2$ greater than or equal to $4$.

Answer 2

Hint: if $n$ is multiple of two odd different primes, $p$ and $q$, then $\varphi(n)$ is a multiple of $(p-1)(q-1)$.