# All Questions

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### square monotonic numbers

monotonic number is a number, which digits are in non-decreasing order. I found by computer that most of these numbers are squares of this numbers 3..34,3..35,3...37,3...367,3...36...7,16...67 My ...
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### If $N = {q^k}{n^2}$ is an odd perfect number given in Eulerian form, does $\sigma(n^2)/q$ divide $2n^2 - \sigma(n^2)$?

Let $\sigma(x)$ be the sum of the divisors of $x$. A number $X$ is called perfect if $\sigma(X) = 2X$. If $N$ is odd and perfect, then $N$ can be written in the Eulerian form $N = {q^k}{n^2}$, where ...
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### How to integrate a function like $(x(1-x))^{-1/3}$?

How to integrate a function like $(x(1-x))^{-1/3}$ within certain limit like $0$ to $1$ ? This question must be having duplicates here but I can't find.Feel free to close if there is a duplicate.
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### “Mean-fields results” in Probability theory

I'm studying a paper on (biological) Neural Networks, and the paper studies some stability properties of an $N$-sized network, and then, as $N$ tends to infinity, it is proven that a "mean-field ...