Results 1 to 2 of 2

Math Help - Euler's totient

  1. #1
    Newbie
    Joined
    Jun 2010
    Posts
    12

    Euler's totient

    Suppose p and q are unequal primes. Prove the following:

    a. pi(p)=p-1
    b. pi(p^2)=p^2-p
    c. pi(p^n)=p^n-p^n-1 where n is a positive integer
    d. pi(pq)=pq-q-p+1 = (p-1)(q-1)
    Last edited by teramaries; June 30th 2010 at 04:54 PM. Reason: mistake
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chiph588@'s Avatar
    Joined
    Sep 2008
    From
    Champaign, Illinois
    Posts
    1,163
    Quote Originally Posted by teramaries View Post
    Suppose p and q are unequal primes. Prove the following:

    a. pi(p)=p-1
    b. pi(p^2)=p^2-p
    c. pi(p^n)=p^n-p^n-1 where n is a positive integer
    d. pi(pq)=pq-q-p+1 = (p-1)(q-1)
    Just list all the numbers less than or equal to the input of  \varphi and count how many are divisible by the input.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Euler totient function
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: February 1st 2010, 09:33 AM
  2. Euler Totient
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: October 11th 2009, 04:38 PM
  3. Euler's Totient Function
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 28th 2009, 07:16 PM
  4. Euler Totient
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: January 29th 2009, 09:46 PM
  5. Euler's totient function
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: December 8th 2008, 08:53 PM

Search Tags


/mathhelpforum @mathhelpforum