Thread: Combinatorial Study of Phi(n)
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Old October 29th, 2009, 10:36 AM
tonio tonio is offline
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Originally Posted by kyldn6 View Post
Prove that \phi(m) is even if m > 2.

and

Find all integers n such that \phi(n) = 12.

For the second one is it possible to do it simply with inspection or is there a formula I'm just missing?

If m=\prod\limits_{n=1}^r p_i^{a_i} \,,\,\,p_i\,\,primes\,,\,\,0<a_i\in \mathbb{N}, then

\phi(m)=m\,\prod\limits_{n=1}^r\left(1-\frac{1}{p_i}\right)

This answers question 1 at once, and for question 2 you have a little maths to do. Enjoy!

Tonio
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