Results 1 to 2 of 2

Math Help - Mappings and Polynomials

  1. #1
    Member Haven's Avatar
    Joined
    Jul 2009
    Posts
    197
    Thanks
    8

    Mappings and Polynomials

    Show that for every mapping g:\mathbb{Z}/p\mathbb{Z}\rightarrow\mathbb{Z}/p\mathbb{Z}, that there exists a polynomial  f(x)\in\mathbb{Z}/p\mathbb{Z}[x] such that  f(a) = g(a) for all a\in\mathbb{Z}/p\mathbb{Z}

    I'm pretty sure Lagrange Interpolation is what is needed here but I'm not sure how to use it.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2008
    From
    Paris
    Posts
    354
    Yes since the sets used are finite with the same cardinal and that \mathbb{Z}_p-\{0\} is a group for \times (I assume p denotes a prime) you can write something like

    f:x\mapsto\sum\limits_{a\in \mathbb{Z}_p}\prod\limits_{k\in\mathbb{Z}_p-\{a\}}\frac{(x-k)g(a)}{(a-k)} , and it is an element of \mathbb{Z}_p[x]
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. automorphism mappings
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 9th 2011, 01:16 PM
  2. composition of mappings
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 17th 2011, 05:59 AM
  3. Linear mappings if polynomials
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: February 23rd 2010, 09:02 AM
  4. Mappings by 1/z
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 16th 2008, 12:22 PM
  5. mappings
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: August 2nd 2008, 11:20 AM

Search Tags


/mathhelpforum @mathhelpforum