Results 1 to 3 of 3

Math Help - Euler Phi primes with just definition of Phi

  1. #1
    Junior Member
    Joined
    Jan 2009
    Posts
    27

    Question Euler Phi primes with just definition of Phi

    So I was given a pretty easy problem
    Calculate \phi(2p) where p is prime.
    Which I can solve with what I have read online:
    * Given \phi(ab) if (a,b)=1, then \phi(a) \phi(b)

    Then it's pretty easy:
    \phi(2p) and since  (2,p)=1, then  \phi(2) \phi(p) = 1*(p-1) = p-1

    But the problem is, in class we haven't proved * ,so we can't use it. Pretty much all we know about  \phi(m) is that it is the number of positive integers wich are less than m and relatively prime to m. AND \phi(p) = p-1 .

    I'm just wondering how I would go about doing this?
    Thanks

    EDIT:
    After some thought and more reading I came to this:

    CASE 1 : if p != 2
    \phi(2p) = \phi(2^1p^1)=
    2p(1-1/2)(1-1/p) = p-1

    Case 2:  p = 2
    \phi(2*2) = \phi(4) =\phi(2^2)=
    4(1-1/2) = 2

    Am I correct in my reasoning?
    Last edited by Th3sandm4n; March 31st 2009 at 09:56 PM. Reason: lightbulb!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Oct 2008
    From
    Guernsey
    Posts
    69
    I think they are expecting you to calculate the value from the definition of \phi(n).

    How many numbers below 2p are coprime to 2?
    How many numbers below 2p are coprime to p?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2009
    Posts
    27
    Quote Originally Posted by SimonM View Post
    I think they are expecting you to calculate the value from the definition of \phi(n).

    How many numbers below 2p are coprime to 2?
    How many numbers below 2p are coprime to p?
    Hmm,
    I get something like
    when p != 2
    How many numbers below 2p are coprime to 2? 2p-2
    How many numbers below 2p are coprime to p? (1/2) 2p
    with overlapping = p-1, but I don't know how to show this other than example values of p?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Euler's Totient Function and the Amount of Primes
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: July 16th 2011, 02:34 PM
  2. Euler path and Euler circuit problem
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 19th 2010, 09:18 PM
  3. Primes and Euler phi-function
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 15th 2010, 03:43 PM
  4. Replies: 0
    Last Post: February 20th 2010, 09:26 AM
  5. Replies: 0
    Last Post: September 17th 2009, 07:44 PM

Search Tags


/mathhelpforum @mathhelpforum