3 problems

For an integer $j\geq 1$, let $\alpha_j$ be the $j$-th metallic mean, so that $\alpha_j^2=j\alpha_j+1$. Let $r_1$ be the unique positive real number such that all terms defined by…

Highly composite minima conjecture. All the integers $n_k$ produced by Theorem 1 are highly composite numbers.

Let $m$ be a positive integer and let $\Lambda^*\subset\mathbb{R}^m$ be a Cantor set. For a continuous function $F^*:\mathbb{R}^m\to\mathbb{R}^m$, write $(F^*)^n$ for its $n$-fold…