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Math Help - Prime Power

  1. #1
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    Prime Power

    Find the sum of all positive integers c such that for some prime a and a positive integer b,
    a^b+b^a=c^a.
    tried taking the second term to the RHS and checked factorizing it. Than i got that a^b is equal to c-b or the remaining term.
    Last edited by geniusgarvil; March 26th 2013 at 09:11 AM.
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  2. #2
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    Re: Prime Power

    this question is from brilliant.org

    this is a simple problem involving basic number theory skills

    answer is 10
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  3. #3
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    Re: Prime Power

    I don't want the answer, i m much more interested in how it came.
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