3 problems

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…

Equivalence conjecture. If $(0,1,\lambda)\sim(0,1,\lambda')$, then either $\lambda$ and $\lambda'$ are both transcendental, or $\lambda$ and $\lambda'$ are conjugate algebraic numb…

Let $d$ be a positive integer, and let … be a linearly independent family with $a_i\in\mathbb{C}$, $e_i\leq d$ for all $i$, and $s\leq ad+b$. Extension conjecture. There are absolu…