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The problem I'm facing is solving the following equation for $p$ given the constants $a_i$ and $b_i$:

$$ \sum_i \frac{a_i}{b_i^p} = 1 $$

Is there a general technique that would allow me to find a value for $p$? If not, are there any heuristic approaches that do not require a computer I can use to find a value for $p$?

  • 4
    The sum is finite or infinite? the $a_i, b_i$ are real numbers, complex numbers, natural numbers? The exponent $p$ is a prime number, or what?2011-10-25

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