6 problems

Let $\{W_n\}_{n\geq 0}$ be the Lehmer numbers, defined by … where $\omega=-1/2+\sqrt{-3}/2$. Komatsu–Liu's conjecture. For any nonnegative integers $n,m$ and positive integer $k$,…

Gaussian Lehmer totient conjecture. For every odd $n$,

Prime-factor conjecture. For every integer $k$ with $2<k$,

Containment conjecture. For every $k\in\mathbb{N}$,

For each natural number $k$, let $L_k$ denote the set of $k$-Lehmer numbers, and let $L_{k+1}\setminus L_k$ be the corresponding difference of successive sets. A Carmichael-number…

Asymptotic independence conjecture. For every $k>1$, the asymptotic behavior of $C_k$ does not depend on $k$ and, in particular,