# Math Help - euler func

1. ## euler func

Prove that phee(n) is even for any n greater than or equal to 3 (here phee(n) is the Euler phee-
function).

2. Originally Posted by anncar
Prove that phee(n) is even for any n greater than or equal to 3 (here phee(n) is the Euler phee-
function).
What do you know about $\phi$ ?

If you know that for $n=p_1^{k_1}.. p_r^{k_r}$ , then:

$\phi(n)=(p_1-1)p^{k_1-1}..(p_r-1)p^{k_r-1}.$

And it follows immeadiatly that if $n>2$ that $\phi$ is even (as if it has an odd prime factor $p_i$, then $(p_i-1)$ is even and so $\phi(n)$ is even, or if it only has even prime factors then it is a power k of 2 greater than the first and $2^{k-1}$ is even)

ZB