4 problems

Let $R$ be a commutative unitary ring. Write $J(R)$ for its Jacobson radical, and let $\textsc{I}(\mathcal{S}_R)$ denote the Erdős–Burgess constant of the multiplicative semigroup…

Wild-number conjecture. The wild numbers are precisely all primes other than $3$. The bibliography records that $3$ is not wild, all other primes below $50$ are wild, and infinitel…

Weak $3x+1$ conjecture. The semigroup ${\cal R}$ contains every positive integer. This is a weak version of the $3x+1$ problem. The bibliography attributes the formulation to Farka…

Let $n>1$ be an integer, and let $R=\mathbb{Z}_n$ be the ring of integers modulo $n$. The modular Erdős–Burgess constant conjecture. … This conjecture gives an exact formula for th…