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Math Help - large exponents with fermats little theorem

  1. #1
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    large exponents with fermats little theorem

    I am trying to solve this problem:

    use Fermat's little theorem to compute 3^302 mod 5.

    I know that with the little theorem you can determine that

    3^4 is congruent to 1 mod 5.

    After that im not really sure how to apply it.

    If anyone could help me with it would be great. thanks.
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  2. #2
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    Quote Originally Posted by jias View Post
    I am trying to solve this problem:

    use Fermat's little theorem to compute 3^302 mod 5.

    I know that with the little theorem you can determine that

    3^4 is congruent to 1 mod 5.

    After that im not really sure how to apply it.

    If anyone could help me with it would be great. thanks.

    The following operations are done modulo 5:

    3^{302}=\left(3^4\right)^{75}\cdot 3^2=1\cdot 3^2 = ...

    Tonio
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