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Math Help - power + modulus

  1. #1
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    lebanon
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    power + modulus

    How can I find "t" such that y = x^t mod 13 and x = y^t mod 13.
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  2. #2
    Junior Member ignite's Avatar
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    Re: power + modulus

    I assume given x and y,you need to find t.
    First observe following trivial solutions:
    1.t=1 for any x and y is a solution.
    2.If x and y both are divisible by 13,then any t will satisfy given conditions.

    Consider the case when both x and y leave same remainder when divided by 13.In this case any t=12k+1 where k is non-negative integer,satisfies given condition.(Using Fermat's Little Theorem).

    For the case x and y leave different remainders,I could conclude that you should only look for t in the set {5,7,11,..}(Set of all numbers whose square leave remainder 1 when divided by 12).I think(?) there does not exist a solution in this case.
    Last edited by ignite; April 22nd 2012 at 01:55 PM. Reason: Solution not complete.
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