Results 1 to 2 of 2

Math Help - Prime numbers and congruence equations.

  1. #1
    Newbie
    Joined
    Jul 2010
    Posts
    9

    Prime numbers and congruence equations.

    Let p be a prime number, and k is a positive integer.

    (a) Show that if x is an integer such that x^2 is congruent to x mod p, then x is congruent to 0 or 1 mod p.

    (b) Show that if x is an integer such that x^2 is congruent to x mod p^k, then x is congruent to 0 or 1 mod p^k.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Swlabr's Avatar
    Joined
    May 2009
    Posts
    1,176
    Quote Originally Posted by DEUCSB View Post
    Let p be a prime number, and k is a positive integer.

    (a) Show that if x is an integer such that x^2 is congruent to x mod p, then x is congruent to 0 or 1 mod p.

    (b) Show that if x is an integer such that x^2 is congruent to x mod p^k, then x is congruent to 0 or 1 mod p^k.
    Write them out in non-modulo form. For example, the first equation reads,

    x^2=x + pr for some r \in \mathbb{Z}. This gives you that x(x-1) = pr and so x \equiv 0 \text{ mod }p or x-1 \equiv 0 \text{ mod }p, as required.

    The second one is approached similarly.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. prime congruence help
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: November 14th 2011, 08:14 AM
  2. Replies: 1
    Last Post: October 22nd 2011, 12:37 PM
  3. Prime Power Congruence
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: April 24th 2009, 08:44 PM
  4. Prime Congruence
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: July 15th 2008, 02:06 PM
  5. Prime Numbers Congruence
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 28th 2007, 04:43 AM

Search Tags


/mathhelpforum @mathhelpforum