Atomic density of arithmetical congruence monoids

Nils Olsson, Christopher O'Neill, Derek Rawling

Consider the set $M_{a,b}=\{n\in {\mathbb{Z}}_{\ge 1}:n\equiv a\mathrm{mod}b\}\cup \{1\}$ for $a,b\in {\mathbb{Z}}_{\ge 1}$. If $a^2\equiv a\mathrm{mod}b$, then $M_{a,b}$ is closed under…