# Math Help - Euler Phi funtion

1. ## Euler Phi funtion

Let $k$ be positive integer $, n=3^k+2$ composite, squarefree

Show that $\Phi(n) \not= 2(3^{k-1}+1)$

2. Originally Posted by wauwau
Let $k$ be positive integer $, n=3^k+2$ composite, squarefree

Show that $\Phi(n) \not= 2(3^{k-1}+1)$

For any natural integer $m=p_i^{a_i}\cdot\ldots\cdot p_k^{a_k}$ , with $p_i$ primes, $0, we have that $\phi(m)=m\prod\limits_{1\le i\le k}\left(1-\frac{1}{p_i}\right)$, so if $2\mid \phi(n)$, then n has to be divisible by a power of 2 greater than 1, and since $n=3^k+2$ then n is odd...

Tonio