On Solvability of an Equation with the Sigma Function

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I have researched this question and need help. In general is there only one solution to the equation $\sigma(nx) = (n+4)x$ for every $n$? Specifically, is there only one solution to $\sigma(5x) = 9x$? ( I know x = 2 is a solution, but is there a way to prove that there are no more?)