Results 1 to 2 of 2

Math Help - Euler Phi funtion

  1. #1
    Newbie
    Joined
    Dec 2009
    Posts
    19

    Euler Phi funtion

    Let  k be positive integer , n=3^k+2 composite, squarefree

    Show that \Phi(n) \not= 2(3^{k-1}+1)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by wauwau View Post
    Let  k be positive integer , n=3^k+2 composite, squarefree

    Show that \Phi(n) \not= 2(3^{k-1}+1)


    For any natural integer m=p_i^{a_i}\cdot\ldots\cdot p_k^{a_k} , with p_i primes, 0<a_i\in\mathbb{N}, we have that \phi(m)=m\prod\limits_{1\le i\le k}\left(1-\frac{1}{p_i}\right), so if 2\mid \phi(n), then n has to be divisible by a power of 2 greater than 1, and since n=3^k+2 then n is odd...

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Euler path and Euler circuit problem
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 19th 2010, 08:18 PM
  2. Replies: 0
    Last Post: February 20th 2010, 08:26 AM
  3. Replies: 0
    Last Post: September 17th 2009, 06:44 PM
  4. exponential funtion
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 22nd 2009, 02:19 PM
  5. Polynomial Funtion HELP PLEASE!!!
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: October 13th 2007, 01:11 PM

Search Tags


/mathhelpforum @mathhelpforum