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Math Help - Modular Arithmatic

  1. #1
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    Modular Arithmatic

    Find the value of x:

    (35-207)= x mod 11

    Can someone show the steps for this answer? I just don't know what to do after I get -172.
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  2. #2
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    Quote Originally Posted by nippy View Post
    Find the value of x:

    (35-207)= x mod 11

    Can someone show the steps for this answer? I just don't know what to do after I get -172.
    (35 - 207) \equiv x~\text{mod 11}

    -172 \equiv x~\text{mod 11}

    So x is the remainder when you divide -172 by 11, ie. it is the solution of the equation:
    -172 = 11 \cdot n + x
    where n is an integer and x is defined to be 0 \leq x < 11.

    I get n = -16 as giving x in the required interval, so
    4 \equiv x~\text{mod 11}

    -Dan
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