3 problems

Let $f(x,y)=(y^2-x^3)/x$. For $Q\in\mathbb{N}_{\geq 2}$, let $C_Q$ be the set defined in the paper for this rational function and quotient $Q$. Nonemptiness and infinitude conjectu…

Let $T$ be the sequence generated by the $6$-GP-free process, and interpret a gap of size $O((\log x)^C)$ as the existence of a constant implicit in the big-$O$ bound, independent…

Rankin's set conjecture. Rankin's set $G^*_3$ has the largest possible density among geometric-progression-free sets which have a density, so