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Math Help - Using Extended Fermat Little Theorem find t remainder when 11^1001 is divided by 12

  1. #1
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    Using Extended Fermat Little Theorem find t remainder when 11^1001 is divided by 12

    Using the Extended Fermat Little Theorem find the remainder when 11
    1001
    is
    divided by 12.
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  2. #2
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    Re: Using Extended Fermat Little Theorem find t remainder when 11^1001 is divided by

    Quote Originally Posted by sbacon1991 View Post
    Using the Extended Fermat Little Theorem find the remainder when 11
    1001
    is
    divided by 12.
    a^{\phi(m)} \equiv 1 \pmod m ,so you have that :

    11^4 \equiv 1 \pmod {12} \Rightarrow (11^4)^{250} \equiv 1 \pmod {12} \Rightarrow 11 \cdot 11^{1000} \equiv 11 \pmod {12}
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  3. #3
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    Re: Using Extended Fermat Little Theorem find t remainder when 11^1001 is divided by

    its surely only true is m is prime and 12 is not prime?
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    Re: Using Extended Fermat Little Theorem find t remainder when 11^1001 is divided by

    Quote Originally Posted by sbacon1991 View Post
    its surely only true is m is prime and 12 is not prime?

    Euler's Theorem
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