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Number theory problem

  1. Nov 17, 2007 #1
    1. The problem statement, all variables and given/known data
    http://math.stanford.edu/~vakil/putnam07/07putnam2.pdf

    I am working on number 2.
    So I want to find 2^70 + 3^70 mod 13.
    I can use Fermat's Little Theorem to reduce the exponent to 10, but I do not know what to do next...


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 18, 2007 #2

    morphism

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    2^2 = 4 and 3^2 = 9

    and 4^5 + 9^5 = (4+9)*something.
     
  4. Nov 18, 2007 #3
    Is that true? Where does that come from?
     
  5. Nov 18, 2007 #4

    morphism

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    You know how there's a formula for a^n - b^n? Well, there's also one for a^n + b^n when n is odd. (a^n + b^n = a^n - (-b)^n.)
     
  6. Nov 18, 2007 #5
    I see. Thanks.
     
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