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Math Help - Deciding whether an integer c is an eth power in Z

  1. #1
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    Deciding whether an integer c is an eth power in Z

    Given any positive integers c and e.

    Any hints?

    Thanks in advance!
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  2. #2
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    Re: Deciding whether an integer c is an eth power in Z

    Hey jsaetrum.

    Can you give an equation or relationship in mathematical form?
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  3. #3
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    Re: Deciding whether an integer c is an eth power in Z

    I tried to express this as a congruence (inverse modulo), i'm not sure it is right, but it seems to be:

    c=m^e

    for any integer m

    and thus satisfying the following:

    m^e \equiv 1\mod(c-1)
    Last edited by jsaetrum; October 15th 2012 at 02:19 AM.
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  4. #4
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    Re: Deciding whether an integer c is an eth power in Z

    I can give you a computer procedure (algorithm) to solve it. It best works out using divisions. (If needed, take "large integers package" like BigInteger from Java or something). Keep dividing c by m, until you get a fraction, or c, or a positive number less than c. Of these outcomes, getting c means, it is a power, other outcomes prove that it is not.

    Salahuddin
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