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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 ...