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Fix $n\in\mathbb N$ and a starting polynomial (or seed) $p_n=a_0+a_1x+\dots+a_nx^n$ with $a_k\in\mathbb Z\ \forall k$ and $a_0a_n\ne0$. Define $p_{n+1},p_{n+2},\dots$ recursively by $p_r = p_{r-1}+...

In this post I consider the following equation involving Pochhammer symbols, $$(n)_m-(k)_l=2\tag{1}$$ for positive integers $n\geq 2$ and $k\geq 2$, and positive integers $m\geq 2$ and $l\geq 2$. ...

Let $n=\frac{B^N-1}{B-1}$. Assume $n$ is congruent to 3 modulo 4. We have the following: If $N$ is 1 modulo 4, then $N$ is quadratic residue modulo $n$ and $-N$ is quadratic non-residue. The square ...

I'm curious about the following diophantine equation from my invention: I don't know if this is in the literature, I wrote it using creativity in an attempt to write a variant of the equation in ...