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Math Help - finding the remainder by mod

  1. #1
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    finding the remainder by mod

    what is the remainder when 2 to the power of 61 is divided by 13?
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  2. #2
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    Quote Originally Posted by air jesus View Post
    what is the remainder when 2 to the power of 61 is divided by 13?
    You want to reduce 2^{61} mod 13.
    Begin with, 2^{12} \equiv 1 ~ (13).
    Raise to the 5th to get 2^{60} \equiv 1 ~ (13).
    Thus, what doth this mean?
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