4 problems

Let $a_{11},a_{22},a_{33},a_{12},a_{13},a_{23},d$ be integers, and consider the generalized Markoff equation … Let $D$ and $A_{11},A_{22},A_{33}$ denote the quantities defined earl…

Let $q$ be a prime power and let an essential triple $(x,y,z)\in\mathbb{F}_q^3$ be the image under $(A,B)\mapsto(\operatorname{tr}A,\operatorname{tr}B,\operatorname{tr}(AB))$ of a…

Positivity conjecture. Every triple $(A,B,C)$ of positive integer solutions to the shadow Markoff equation can be obtained from an initial triple with $(\alpha:\beta:\gamma)$ a rat…

Classification conjecture.