Euler function-totient

1. Nov 5, 2008

AlexHall

Hello, can anyone help with this question? Thank you.

Let n even perfect number and q prime. Show that n/Φ(n)=2q/q-1.

Φ(n) is the Euler function-totient (the number of positive integers less than or equal to n that are coprime to n)

I have tried euler-euclid theorem but could not get it.

2. Nov 5, 2008

Office_Shredder

Staff Emeritus
Re: urgent help

2q/(q-1) is different for different primes q, so you must have some additional condition on what q is (unless you really meant without the parentheses, in which case 2q/q-1 = 1 which makes no sense). Unless you're trying to show such a q exists?

3. Nov 6, 2008

AlexHall

Re: urgent help

phi(n)=phi[2^(k-1)q] where q=(2^k)-1

phi(n)=phi(2^(k-1))phi(q)=phi(2^(k-1))(q-1)

Is there any property I can use to finish this?

4. Nov 6, 2008

Dick

Re: urgent help

What's phi(2^(k-1))? There's a formula for phi for powers of a prime. (It's also the number of odd integers less than 2^(k-1)).