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Math Help - Positive integers

  1. #1
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    Positive integers

    Lost on this one

    let a, b and c be positive integers such that a^(b+c) = b^(c)c. Prove that b is a divisor of c, and that c is of form d^(b) for some positive integer d.
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  2. #2
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    Re: Positive integers

    a^{b+c}=b^cc
    hence b|a
    or a=r.b
    for some integer r
    (rb)^{b+c}=b^cc

    r^{b+c}b^bb^c=b^cc

    r^{b+c}b^b=c

    hence [Tex]b|c or c=s.b for some integer s

    r^{(1+s)b}b^b = c

    (r^{1+s}b)^b = c
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