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Math Help - Fermat's little theorem

  1. #1
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    Exclamation Fermat's little theorem

    Hello, I have a test tomorrow and this may or may not be on that test.
    Anyway, I can't for the life of me understand what is being asked here:

    Use Fermat's little theorem to compute:
    3^302 mod 5, 3^302 mod 7, 3^302 mod 11

    I've tried to look this up online, but I can't find anything. I just don't understand the connection to Fermat's little theorem, which is :
    for p prime and a a pos. integer:
    a^(p-1) CONGRUENT 1 (mod p)

    Any help would be very appreciated!!
    Thanks so much!
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  2. #2
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    Quote Originally Posted by epsilon View Post
    Hello, I have a test tomorrow and this may or may not be on that test.
    Anyway, I can't for the life of me understand what is being asked here:

    Use Fermat's little theorem to compute:
    3^302 mod 5, 3^302 mod 7, 3^302 mod 11

    I've tried to look this up online, but I can't find anything. I just don't understand the connection to Fermat's little theorem, which is :
    for p prime and a a pos. integer:
    a^(p-1) CONGRUENT 1 (mod p)

    Any help would be very appreciated!!
    Thanks so much!
    3^4 = 1 (mod 5) by Fermat theorems.
    So (raise to the 75) both sides,
    3^300 = 1 (mod 5)
    Multiply 3^2 both sides,
    3^302 = 3^2 = 9 = 4 (mod 5)

    The same thing with the others.
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  3. #3
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    Oct 2007
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    Thanks!

    Thank you very much! You've put my mind to ease about the test tomorrow.
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  4. #4
    dpe82
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    Quote Originally Posted by epsilon View Post
    Thank you very much! You've put my mind to ease about the test tomorrow.
    You don't happen to be a Math 240 student at UW-Madison, do you?
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