I have an hypothesis and I tried a lot of prime numbers on it and it worked , so if this hypothesis is correct ; How can it contribute to math ? Let $y$ be a non-zero natural number; Let $p_y$ (X) be the $y$th natural number, indexing from 1. E.g. $p_1 = 2$. Let $\sigma_1(y)$ be the divisor sum ...

A year ago I started working on Conway's 99-graph problem. I want to verify the following results of this work to continue my struggling. Are there any crucial or minor mistakes? Since there is a lot of text, I will appreciate your remarks on some of five parts. $$\color{blue}{\text{I. Conway's 9...

HERE is one. It came to the front page again today. Over the years, many posts have asked this same question: compute $\displaystyle\int \frac{dx}{1+x^4}$ . They have all been merged into this one. It should be reopened. It can serve as the target for any future duplicates.

Please see this wiki subsection before commenting: https://en.wikipedia.org/wiki/Collatz_conjecture#Extensions_to_larger_domains So over all integers as inputs, the Collatz conjecture is, roughly speaking, that under iteration by the Collatz function $f$, you will eventually reach one of the loo...

Let $M = 2\Bbb{Z} + 1$ or $2 \Bbb{N} + 1$ where $0 \in \Bbb{N}$, this approach will probably play well with both forms. Define the shortcut Collatz function to be: $$ f : M \to M \\ f(x) = \dfrac{3x + 1}{2^{\nu_2(3x + 1)}} $$ where $\nu_2(z)$ is the common notation meaning the maximum exponent $...