2 problems

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The roots-of-unity and irrational-angle conjecture for complex Markov triples
Let $(z_1,z_2,z_3)$ be a triple of complex roots of unity, and let $n$ be the minimal positive integer such that $z_i^n=1$ for each $i$ . Write the arguments as fractions of a full…
Conjectureopencomplex-numbers markov-numbers mutation-dynamicsarXiv posted 2 days ago
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The six-shadow conjecture for Markov numbers
A Markov number is a number appearing in a Markov triple generated by mutation. For an initial triple with distinct entries, the mutation tree can have distinct shadows associated…
Conjectureopenmarkov-numbers mutation-dynamicsarXiv posted 2 days ago

The roots-of-unity and irrational-angle conjecture for complex Markov triples