6 problems

A Markov number is a positive integer occurring in a Markov triple, that is, a triple of positive integers satisfying the Markov equation. A Markov triple is ordered here as…

Fix $\sigma\in \mathfrak S_3$, and let $k_1,k_2,k_3$ be nonnegative integers. Consider the generalized Markov tree $\mathrm{M}\mathbb T(k_1,k_2,k_3,\sigma)$. For any irreducible fr…

Fix $\sigma\in \mathfrak S_3$ and consider the Markov tree $\mathrm{M}\mathbb T(0,0,0,\sigma)$. For any irreducible fractions $t,s\in[0,1]$, let $n_t$ and $n_s$ be Markov numbers w…

Let $\mathcal M_{0,0,0}$ denote the classical discrete Markov spectrum, and let $\mathcal L(\alpha)$ denote the Markov-Lagrange value associated with an irrational $\alpha$. Two ir…

Exact Hausdorff distance conjecture. The Hausdorff distance between $M$ and $L$ is precisely $\delta_0$.

Moreira's question. For every $\delta>0$, one has