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Math Help - Equation with exponents

  1. #1
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    Equation with exponents. Not solved yet. Please help

    Hi!

    I was wandering if anyone of you could help me solve the following equation:

    2^x + 5^y = k^2

    where x, y, k are integers.

    I know the best way to solve it is to use modulo but, to be honest, I don't really know how modulo works in such equations.

    Maybe you have another approach to this task - please share it
    Last edited by gollum; September 18th 2011 at 01:05 AM.
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  2. #2
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    Re: Equation with exponents

    Here's 2:
    (2,1,3): 2^2 + 5^1 = 3^2

    (3,0,3): 2^3 + 5^0 = 3^2

    Probably loads more...
    Perhaps someone else will have a "trick" for you...
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  3. #3
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    Re: Equation with exponents

    Thanks
    I do hope someone will have a trick for me, because there needs to be a proof that there aren't any more solutions.
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  4. #4
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    Re: Equation with exponents

    r u sure there r not any more?
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  5. #5
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    Re: Equation with exponents

    Quote Originally Posted by islam View Post
    r u sure there r not any more?
    Well, I wrote short program to find these: contrary to what
    I had asssumed, couldn't find any!
    Why do you think there's more, islam? Got an example?
    By the way, for your benefit, I suggest you start using
    are (not r) and you (not u): may cause problems if you're
    typing a math problem with variables.
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