$p$-adic quotient sets
  For $A \subseteq \mathbb{N}$, the question of when $R(A) = \{a/a' : a, a' \in A\}$ is dense in the positive real numbers $\mathbb{R}_+$ has been examined by many authors over the years. In contrast, the $p$-adic setting is largely unexplored. We investigate conditions under which $R(A)$ is dense in the $p$-adic numbers. Techniques from elementary, algebraic, and analytic number theory are employed in this endeavor. We also pose many open questions that should be of general interest. 
Stephan Ramon Garcia, Yu Xuan Hong, Florian Luca, Elena Pinsker, Carlo   Sanna, Evan Schechter, Adam Starr
math.NT