3 problems

Strong Markoff uniqueness conjecture. Each of the badly approximable irrationals $\xi$ corresponding to a Markoff triple $(x,y,z)$ has a different field of definition…

Markoff uniqueness conjecture. Any positive integer $z$ occurs at most once as the largest element of a Markoff triple. Consequently, the numbers $\xi$ with approximability values…

Begin with an oriented triangulation of the once-punctured torus described in the source, and retain $e$ as a formal variable rather than setting it equal to $1$. Iterated flips in…