Results 1 to 5 of 5

Math Help - Help solve this

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    6

    Help solve this

    Show that for any integer m>1, a^m≡a^(m-φ(m))mod(m).Help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Bruno J.'s Avatar
    Joined
    Jun 2009
    From
    Canada
    Posts
    1,266
    Thanks
    1
    Awards
    1
    What is a^{\phi(m)}\mod m?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2010
    Posts
    6

    Help solve this

    For any integer m>1,φ(m) is the number of integers not greater than m and are relatively prime to m.I think I can re frame my question if you don't understand the former;For any integer m>1,show that m divides a^m-a^(m- φ(m)) for all integers a.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member Bacterius's Avatar
    Joined
    Nov 2009
    From
    Wellington
    Posts
    927
    Quote Originally Posted by ogajawasungu View Post
    For any integer m>1,φ(m) is the number of integers not greater than m and are relatively prime to m.I think I can re frame my question if you don't understand the former;For any integer m>1,show that m divides a^m-a^(m- φ(m)) for all integers a.
    I think Bruno J. was trying to hint you a property of this function. Think of Euler's Generalization.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2010
    Posts
    6
    I thought of it earlier,but because Euler's generalization requires that (a,m)=1,this kind of problem became a nightmare to me.I also tried by induction proof and got stuck.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. need to solve summation equation to solve sum(x2)
    Posted in the Statistics Forum
    Replies: 2
    Last Post: July 16th 2010, 11:29 PM
  2. Replies: 1
    Last Post: June 9th 2009, 11:37 PM
  3. how do I solve this?
    Posted in the Calculus Forum
    Replies: 5
    Last Post: January 22nd 2009, 07:21 PM
  4. How could i solve?
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 2nd 2009, 03:18 PM
  5. Solve for x
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: January 1st 2009, 01:33 PM

Search Tags


/mathhelpforum @mathhelpforum