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Math Help - How do I simplify this mod question further?

  1. #1
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    How do I simplify this mod question further?

    Use the fact that 4001 is a prime to compute r \equiv 457^{43743747}~mod~4001, and find an integer k such that r^k\equiv 457~mod~4001.

    So I used Fermat's little theorem to reduce the problem initially:

    43743747=4000\times 10935 + 3747

    \therefore 457^{4000\times 10935}457^{3747}~mod~4001

    reduces to just:

    457^{3747}~mod~4001

    How can I reduce things further without taking all day?

    Thanks.
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  2. #2
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    Re: How do I simplify this mod question further?

    Do I just need to keep taking out factors of 3747 and computing the smaller numbers mod 4001 until I have reduced it? The largest exponent I can raise 457 to that doesn't produce a number in scientific notation with my calculator is 3 :S
    Last edited by terrorsquid; November 15th 2011 at 01:51 PM.
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