3 problems

Let $S$ be a finite set of primes with $\#S\geq2$, and let $\mathcal{G}$ be its $S$-unit graph. A cycle is nondegenerate if its edge differences have no proper nonempty zero subsum…

Let $S$ be a finite nonempty set of primes. Let $\mathcal{G}$ be the graph with vertex set $\mathbb{Q}$ in which two rationals are adjacent when their difference is an $S$-unit. A…

Szalay–Ziegler conjecture. No $\{p,q\}$-Diophantine quadruple exists.