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Homework Help: How do I prove that 5 divides x^5 - x?

  1. Feb 10, 2010 #1
    How do I prove that 5 divides x^5 - x??

    How do I prove that 5 divides x^5 - x??
     
  2. jcsd
  3. Feb 10, 2010 #2

    CRGreathouse

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    Re: How do I prove that 5 divides x^5 - x??

    Compute the fifth powers mod 5.
     
  4. Feb 10, 2010 #3

    CompuChip

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    Re: How do I prove that 5 divides x^5 - x??

    Let me give you a hint: checking it for x = 0, 1, 2, 3 and 4 suffices.

    (In fact, as 4 = -1 (mod 5) and 3 = -2 (mod 5), you can see that only x = 0, 1, 2 will do).

    I'll let you figure out why.
     
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