Results 1 to 2 of 2

Thread: incongruent integers

  1. October 8th 2009, 04:23 PM #1
    dori1123
    dori1123 is offline
    Member
    Joined
    Sep 2008
    Posts
    166

    incongruent integers

    Suppose that x \in \mathbb{Z_p^\times} has order p-1. Prove that the integers x^1, x^2, ..., x^{p-1} are incongruent mod p.
    Follow Math Help Forum on Facebook and Google+
  2. October 8th 2009, 05:43 PM #2
    Bruno J.
    Bruno J. is offline
    MHF Contributor Bruno J.'s Avatar
    Joined
    Jun 2009
    From
    Canada
    Posts
    1,266
    Awards
    1
    MHF Donor
    Quote Originally Posted by dori1123 View Post
    Suppose that x \in \mathbb{Z_p^\times} has order p-1. Prove that the integers x^1, x^2, ..., x^{p-1} are incongruent mod p.
    This is precisely what it means for x to have order p-1.
    Follow Math Help Forum on Facebook and Google+
« proof of infinite n's s.t. sqrt(n) = irrational | Greastest Common Divisor »

Similar Math Help Forum Discussions

  1. incongruent solutions
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: October 16th 2010, 06:27 PM
  2. incongruent primitive roots
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: November 9th 2008, 10:14 AM
  3. incongruent integers
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: November 9th 2008, 10:00 AM
  4. incongruent solutions to (mod n)
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: June 4th 2008, 03:28 PM
  5. 2^n is incongruent to 1 (mod n)
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: January 13th 2007, 02:11 PM

Search Tags


/mathhelpforum @mathhelpforum