n is perfect even number, q prime: show n/phi(n) = 2q/(q-1)

[AlexHall]

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

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

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

 

[mmm4444bot]

Hello Alex:

Please give us a clue as to what you already know about these types of exercises. Show any work and reasoning that you've able to accomplish, so far.

If you already understand what the exercise is asking, then are you able to say something about why you're stuck?

(Also, please read the post titled, "Read Before Posting", if you have not already done so.)

Cheers,

~ Mark

 

[AlexHall]

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?