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Modular Arithmetic Proof with exponents

  1. Sep 27, 2011 #1
    1. The problem statement, all variables and given/known data

    Let p be a prime number.
    Prove:

    (a+b)^p modp = [(a^p modp) + (b^p modp)]modp


    2. Relevant equations

    modular arithmetic.


    3. The attempt at a solution

    I honestly haven't the slightest clue.
    Would induction be my best bet here?
    If so, when I suppose the statement is true for (k+1), n isn't always prime anymore.

    I used to be a biochem major and just switched into algebra, so I'm sorry if I seem retarded, I'm just very behind! Help please!
     
  2. jcsd
  3. Sep 27, 2011 #2

    Dick

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    No, induction isn't your best bet for the very good reason you mention. Think about the binomial expansion of (a+b)^p.
     
    Last edited: Sep 27, 2011
  4. Sep 27, 2011 #3

    Dick

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    Write the binomial expansion without knowing what p is. Just write it symbolically. Can you show many of the binomial coefficients are divisible by p?
     
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