5 problems

Let $d\in\mathbb{N}_{\geq 2}$, let $\zeta$ be a primitive $d$th root of unity, and let $A_d$ be the set defined earlier in the paper. Let $\mathcal H(n,2\zeta)$ denote the correspo…

Let $(n_k)$ be the sequence defined earlier in the paper, and let $\mathcal H(n,1)$ be the associated Hankel determinant. Monotonicity conjecture. The sequence of absolute values…

Let $\mathcal H(n,1)$ denote the Hankel determinant studied in the paper. For each fixed integer $k\geq 0$, consider the values with index $n=2^m+k$. Asymptotic product formula con…

Finite-exception conjecture. The residual finite set is

Bennett–Bugeaud–Mignotte conjecture. The only solutions are