2 problems

Lubinsky's conjecture. The set $S$ is empty. This conjecture was disproved: Verschueren, and independently Grepstad, Kaltenböck and Neumüller, proved that the Golden Ratio…

For $alpha\in[0,1)$, let … where $[0;a_1,a_2,\ldots]$ is the continued fraction expansion of $alpha$. Also define … with…