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Math Help - How to solve a^x mod b = c?

  1. #1
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    How to solve a^x mod b = c?

    How to solve a^x mod b = c for x minimum integer solution.

    With known integers a, b, and c.
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  2. #2
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    Jul 2010
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    Re: How to solve a^x mod b = c?

    If b=1,2,4,p^\alpha,2p^\alpha with \alpha\ge 1 and p an odd prime, then b has a primitive root g \mod b.
    If (a,b)=(c,b)=1 then x ind _g a\equiv ind _g c \pmod {\phi(b)} a linear congruence in x.
    If d=(ind _g a,\phi(b))| ind _g c then there are exactly d solutions.

    Then start by factoring b. If b has a factor 2^f with f\ge 3 then solve the equation \mod 2^f first.
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