4 problems

Graham's conjecture. The set $S(t,\alpha)$ is complete for every

Erdős's conjecture. There is a constant $c$ such that every increasing sequence satisfying

Let $A i ewline$ be a subset of $mathbb{N}$, let $mathbb{T}=mathbb{R}/mathbb{Z}$, and for $x i ewlinebashtext{in}mathbb{R}$ let $Vert xVert$ denote the distance from $x$ to the nea…

Burr–Erdős–Graham–Li conjecture. The authors conjecture that the corresponding union of sets of the form $\Gamma(a)$ is complete.