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mathworker
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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 into \(\displaystyle X^2\)
It will be helpful if someone supply some hints :)
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 into \(\displaystyle X^2\)
It will be helpful if someone supply some hints :)
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