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Math Help - How to solve large mod equation?

  1. #1
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    How to solve large mod equation?

    I have no problem solving smaller equations and understand the logic but don't know how to go about solving a large one such as the one below:

    21^16 mod 17

    Please show me the process in which to find the answer.

    Thanks for your help
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  2. #2
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    Quote Originally Posted by dragstang86 View Post
    I have no problem solving smaller equations and understand the logic but don't know how to go about solving a large one such as the one below:

    21^16 mod 17

    Please show me the process in which to find the answer.

    Thanks for your help

    Google, or read in a book, about Fermat's Little Theorem: 21^{16}=4^{16}=1\!\!\pmod {17}

    Tonio
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  3. #3
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    Thanks for the input. I read about Fermat's Little Theorem but I must be missing something. The way I understand it is if 16 was prime then 21^16 would equal 21 mod 16 which would leave me with (21 mod 16) mod 17 but 16 is not prime. What am I missing?
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  4. #4
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    Quote Originally Posted by dragstang86 View Post
    Thanks for the input. I read about Fermat's Little Theorem but I must be missing something. The way I understand it is if 16 was prime then 21^16 would equal 21 mod 16 which would leave me with (21 mod 16) mod 17 but 16 is not prime. What am I missing?

    Read here Fermat's little theorem - Wikipedia, the free encyclopedia the first few lines, in particular line 6.

    Tonio
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