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Math Help - Modular Inverses

  1. #1
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    Modular Inverses

    Hi is there a general formula to find the inverse modulo of "a modulo n"...
    i know its denoted as a^{-1} and
    a.a^{-1} = 1 mod n

    for example if a=29 and n = 78 then the inverse is 35 since: 29.35 = 1 mod 78...

    (a)
    but HOW DO U CALCULATE THE INVERSE? is there a formula?? please help me out here?

    (b)
    and how can this be used to solve 43 modulo 125, hence solve 43x = 3 mod 125

    thanks
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  2. #2
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    Quote Originally Posted by smoothman View Post
    Hi is there a general formula to find the inverse modulo of "a modulo n"...
    i know its denoted as a^{-1} and
    a.a^{-1} = 1 mod n

    for example if a=29 and n = 78 then the inverse is 35 since: 29.35 = 1 mod 78...

    (a)
    but [COLOR=Red]HOW DO U CALCULATE THE INVERSE? [COLOR=Black]is there a formula?? please help me out here?

    (b)
    and how can this be used to solve 43 modulo 125, hence solve 43x = 3 mod 125
    ]
    You can apply Euclid's algorithm, that is what I do when it is big numbers.
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