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
$\begingroup$
$\endgroup$
1
asked Feb 13, 2016 at 6:39
-
1$\begingroup$ Related : math.stackexchange.com/questions/702550/… $\endgroup$– lab bhattacharjeeCommented Feb 13, 2016 at 10:35
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
4
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 $4$.
answered Feb 13, 2016 at 7:16
-
1$\begingroup$ Not all odd primes are equally good for us. $\endgroup$ Commented Feb 13, 2016 at 8:34
-
$\begingroup$ Thanks alot this is almost done $\endgroup$ Commented Feb 14, 2016 at 5:41
-
$\begingroup$ Careful because I forgot some cases... $\endgroup$ Commented Feb 14, 2016 at 14:27
-
$\begingroup$ May be the powers of odd primes $\endgroup$ Commented Feb 14, 2016 at 14:37
$\begingroup$
$\endgroup$
0
Hint: if $n$ is multiple of two odd different primes, $p$ and $q$, then $\varphi(n)$ is a multiple of $(p-1)(q-1)$.
