8 problems

Markov Uniqueness conjecture. If $\max(a,b,c)=\max(a',b',c')$, then there exists a permutation $\sigma\in\mathfrak{S}_3$ such that

For a prime $p$, let $\mathbb{F}_p$ be the finite field with $p$ elements, and let the Markov graph over $\mathbb{F}_p$ be the graph associated with the Markov equation over that f…

A Markov number is an integer occurring in a Markov triple, and a Markov fraction is a rational number associated with the Markov fraction tree. Springborn's unicity conjecture. Fo…

Let $(x,y,z)$ be a positive integer solution of the Markov Diophantine equation, obtained in the case $k_1=k_2=k_3=0$. Two triplets are said to have a common maximum if their large…

Strong Approximation Conjecture. All non-zero solutions of the Markov equation modulo $p$ come from Markov triples.

Let $m>2$ be a Markov number, meaning an integer belonging to a triple of positive integers satisfying … For coprime positive integers $a<b$, write $b/a=[a_1,a_2,\ldots,a_n]$ as a…

Let $m>2$ be a Markov number, meaning an integer belonging to a triple of positive integers satisfying … For coprime positive integers $a<b$, the palindromification of the snake gr…

Markov-number uniqueness conjecture. One has