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Fermit's theorem

  1. Apr 9, 2010 #1
    How to use fermit's thereom in finding remainder of a number when divided by another number ???

    (eg remainder of 52005 when divided by 4010 ????)
  2. jcsd
  3. Apr 9, 2010 #2
    How did you arrive at such a problem? Fermat's (little) theorem deals prime powers.
  4. Apr 9, 2010 #3
    I'm assuming you don't know or don't want to use Euler's theorem.

    Note 4010 = 2*5*401.

    Can you find integers a,b,c such that
    5^{2005} &\equiv a \pmod 2 \\
    5^{2005} &\equiv b \pmod 5 \\
    5^{2005} &\equiv c \pmod {401}
    ? (perhaps using Fermat's little theorem)

    If you can, then you can use these results and the Chinese remainder theorem to find 5^2005 modulo 2*5*401.
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