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Let $p_n$ be the $n$th prime, and define
$$g_n:=p_{n+1}-p_n.$$
The Prime Number Theorem gives

Let $R$ be a ring, and let $M_R$ and $N_R$ be right $R$-modules. I was taught to always write module homomorphisms on the opposite side from scalars. Thus, a map $\varphi\in {\rm Hom}_R(M,N)$ would be written on the left side of elements of $M$. The...

This question is linked to a prior one.
Language: Mono-sorted first order logic with equality and additional primitives of $\xi$ signifying is the order of, and the binary relation $ [ \ ] $ signifying predication that is $p[x]$ to be read as $p$ predicates $x$, or equivalently as $x$ is predicated...

In my investigation on higher power Diophantine triples (arxiv, related MO question), I considered the following equation in rationals$$\tag{1} \label{cubic_sum_square_product}x^3+y^3=z^3+1, \\xyz=\square,$$where by $\square$ I mean a rational square...