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Math Help - Remainders

  1. #1
    Vey
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    Remainders

    Hey, I need to calculate the remainder when

    (41^13 + 37^6) is divided with 13 and I'm kinda lost.

    Thanks in advance!
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  2. #2
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    Quote Originally Posted by Vey View Post
    Hey, I need to calculate the remainder when

    (41^13 + 37^6) is divided with 13 and I'm kinda lost.

    Thanks in advance!

    Hints:

    (1) For any a\in\mathbb{Z}\,,\,\,a^p=a\!\!\!\!\pmod p\,,\,\,p a prime number

    (2) a^{2k}=(-a)^{2k}\!\!\!\!\pmod p , for any integer k.

    (3) 2^6=-1=12\!\!\!\!\pmod{13}

    Tonio
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  3. #3
    Senior Member Shanks's Avatar
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    by the fermat theorem, the first term leaves a remainder of 2 divided by 13.
    for the second term, notice that 37 leaves a remainder of -2 divided by 13, you can take it from here.
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