Results 1 to 2 of 2

Math Help - Congruences

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    46

    Congruences

    Let a,m be integers with m>0, gcd(a,m)=1 and gcd(a-1,m)=1. Prove that a^(phi(m)-1)+a^(phi(m)-2)+...+a^2+a+1 = 0 mod m
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Aug 2008
    Posts
    80
    Hello,

    (a^(phi(m)-1)+a^(phi(m)-2)+...+a^2+a+1)(a-1)=a^(phi(m))-1.
    Now, divide by a-1 (which is prime relative to m.)

    Bye.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Congruences
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: March 11th 2010, 12:52 PM
  2. Congruences
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: May 7th 2009, 02:26 PM
  3. Congruences
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 18th 2009, 05:12 AM
  4. More congruences
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: March 17th 2009, 10:40 PM
  5. Congruences
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: October 6th 2008, 06:18 PM

Search Tags


/mathhelpforum @mathhelpforum