# Math Help - Help with euler-phi function

1. ## Help with euler-phi function

Hi can someone help me with this question,

"Give a brief argument to show that phi(n) is even for all n>2"

2. Originally Posted by BruceBronson
Hi can someone help me with this question,

"Give a brief argument to show that phi(n) is even for all n>2"
If $\gcd(a,b)=1$ then $\phi(ab)=1$. If $n>1$ and $p$ an odd prime divisor of it we can write $n=p^kj$ where $j$ not divisible by $p$. Then $\phi(n) = \phi(p^k)\phi(j)$. Thus, $\phi (p^k) = p^{k}-p^{k-1}$ which is even. Now finish the argument.

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