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Math Help - remainder modulo

  1. #1
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    remainder modulo

    find the remainder of 14^85 mod 49?

    i know that this is 14^85 congruent to a mod 49, where we want to find a.
    since (14,49) =7, it means that a is divisible by 7. then what happens next?
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  2. #2
    MHF Contributor

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    Re: remainder modulo

    note that 14 = 2*7 and 1485 = (285)(785) = (285)(7)(784) = (285)(7)(72)42

    = (285)(7)(49)42.

    it stands to reason therefore that 49 divides 1485, which is therefore 0 (mod 49).
    Thanks from alexandrabel90
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