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

function).

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- Dec 8th 2007, 08:53 PManncareuler func
Prove that phee(n) is even for any n greater than or equal to 3 (here phee(n) is the Euler phee-

function). - Dec 9th 2007, 07:43 AMConstatine11
What do you know about $\displaystyle \phi$ ?

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

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

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

ZB