Results 1 to 2 of 2

Math Help - Characteristic of a field

  1. #1
    Junior Member
    Joined
    May 2008
    Posts
    70

    Characteristic of a field

    let F be a field with characteristic p, a prime. show that (a+b)^p = a^p + b^p for all a,b in F.

    Using pascal's triangle it's easy to show for the first few primes that this is true, yet I don't know how to prove it for all primes, p. I was thinking of using induction, but don't know exactly how to go about doing that. Any help would be appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by Coda202 View Post
    let F be a field with characteristic p, a prime. show that (a+b)^p = a^p + b^p for all a,b in F.

    Using pascal's triangle it's easy to show for the first few primes that this is true, yet I don't know how to prove it for all primes, p. I was thinking of using induction, but don't know exactly how to go about doing that. Any help would be appreciated.
    This question has been posted on MHF before many times. There are two hints.

    Hint 1: Use binomial theorem.

    Hint 2: Note that p divides {p\choose j} for 0 < j < p.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Field with Characteristic 0
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 20th 2010, 11:49 AM
  2. Infinite Field With Characteristic 5?
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 18th 2010, 11:10 AM
  3. field, characteristic, surjective
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 14th 2009, 08:56 PM
  4. [SOLVED] Find all p-th roots in field of characteristic p
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: February 9th 2009, 04:01 AM
  5. Field Characteristic
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: January 25th 2007, 04:52 PM

Search Tags


/mathhelpforum @mathhelpforum