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Math Help - residue

  1. #1
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    least residue

    5^(10) (mod 11)
    5^(12) (mod 11)
    1945^(12) (mod 11)

    i need help on how to start step-by-step
    Last edited by mr fantastic; February 17th 2009 at 03:56 AM. Reason: Merged posts
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  2. #2
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    Quote Originally Posted by Sally_Math View Post
    least residue

    5^(10) (mod 11)
    5^(12) (mod 11)
    1945^(12) (mod 11)

    i need help on how to start step-by-step
    You should not know 5^10 = 1(mod 11) by Fermat's little theorem, and so, 5^(12) = 5^2 = 3 (mod 11).
    Try the same thing with 1945.
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