Results 1 to 2 of 2

Math Help - Congruences modulo p

  1. #1
    Newbie
    Joined
    Nov 2006
    Posts
    14

    Congruences modulo p

    Let a and b be integers not divisible by the prime number p. If a^p = b^p (mod p), prove that a^p = b^p (mod p^2).
    Please help me!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Okay, here is the proof below.
    This example insipired me to create my own challenge.

    Theorem If p does not divide a and b, such that,
    a^p=b^p (mod p) then a^(p^2)=b^(p^2) (mod p^2).

    Try to show that.
    Attached Thumbnails Attached Thumbnails Congruences modulo p-picture24.gif  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Modulo of squares = modulo of roots
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: December 1st 2009, 09:04 AM
  2. congruences
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: September 5th 2009, 10:59 AM
  3. More congruences
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: March 17th 2009, 10:40 PM
  4. congruences
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: November 7th 2007, 09:14 AM
  5. Help with modulo and congruences
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: February 19th 2007, 07:39 AM

Search Tags


/mathhelpforum @mathhelpforum