Results 1 to 3 of 3

Math Help - Number theory

  1. #1
    Junior Member
    Joined
    Feb 2006
    From
    Canada
    Posts
    45

    Exclamation Number theory

    Show that if a is an integer, then 3 divides (a to the power 3) - a

    I don't know how to use the mathematical software to express the question, I apologize for any inconvenience. Thanks for helping me out.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by suedenation View Post
    Show that if a is an integer, then 3 divides (a to the power 3) - a

    I don't know how to use the mathematical software to express the question, I apologize for any inconvenience. Thanks for helping me out.
    a^3-a=a(a^2-1)=a(a-1)(a+1)

    that is it is the product of three consecutive integers. But in every set
    of three consectutive integers at least one is divisible by 3.

    Hence a^3-a is divisible by 3.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Furthermore, this is a faboulus beautiful elegant powerful super and amazing theorem of Fermat (my favorite mathemation).

    That,
    a^p-a
    Is always divisible by p
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Textbooks on Galois Theory and Algebraic Number Theory
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: July 8th 2011, 07:09 PM
  2. Number Theory
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: May 19th 2010, 08:51 PM
  3. Number Theory
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: February 16th 2010, 06:05 PM
  4. Replies: 2
    Last Post: December 18th 2008, 06:28 PM
  5. Number theory, prime number
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: September 17th 2006, 09:11 PM

Search Tags


/mathhelpforum @mathhelpforum