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  1. MHB Craftsman
    mathworker's Avatar
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    May 2013
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    Hello I am reading "The Theory of Numbers, by Robert D. Carmichael" and stuck in an exercise problem,

    Find numbers x such that the sum of the divisors of x is a perfect square.

    I know sum of divisors of a $ \displaystyle x = p_1^{{\alpha}_1}.p_2^{{\alpha}_1}...p_n^{{\alpha}_1}$ is

    Sum of divisors $ \displaystyle =\prod{\frac{p_i^{{\alpha}_i+1}-1}{p_i-1}} $

    But couldn't proceed further on how resolve the product in to $ \displaystyle X^2$

    It will be helpful if someone supply some hints
    Last edited by mathworker; May 7th, 2016 at 09:43. Reason: correction

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