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Math Help - Fermat's little theorem help!

  1. #1
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    Unhappy Fermat's little theorem help!

    What is the remainder when 132^75 is divided by 37?

    I really am confused even though the problem gives a hint that I should use Fermat litle theorem
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  2. #2
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    Quote Originally Posted by nhunhu9 View Post
    What is the remainder when 132^75 is divided by 37?

    I really am confused even though the problem gives a hint that I should use Fermat litle theorem
    Do you know Fermat's little theorem?
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    Quote Originally Posted by nhunhu9 View Post
    What is the remainder when 132^75 is divided by 37?

    I really am confused even though the problem gives a hint that I should use Fermat litle theorem

    132^{75}=\left(132^{37}\right)^2\cdot 132 , and now apply FlT .

    Tonio
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    Quote Originally Posted by nhunhu9 View Post
    What is the remainder when 132^75 is divided by 37?

    I really am confused even though the problem gives a hint that I should use Fermat litle theorem
    Here is the theorem:

    a^{p-1}\equiv 1 \ \mbox{(mod p)}
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  5. #5
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by dwsmith View Post
    Here is the theorem:

    a^{p-1}\equiv 1 \ \mbox{(mod p)}
    If a\ne zp.
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