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A perfect number is a positive integer that is equal to the sum of its proper positive divisors.

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Help with R. Ryan's "A simpler dense proof regarding the abundancy Index."

I'm reading Richard Ryan's article "A simpler dense proof regarding the abundancy index" and got stuck in his proof for Theorem 2. The Theorem is stated as follows: Suppose we have a fraction of the f …
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Help with R. Ryan's "A simpler dense proof regarding the abundancy Index."

It is actually possbile to show that $b$ is odd with a direct proof, without the contradiction I didn't understand. From the assumptions $n$ odd and $I(b)=\frac{\sigma(b)}{b}=\frac{2n-1}{n}$ with an o …
jvkloc's user avatar
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