Bases which admit exactly two expansions

Yi Cai, Wenxia Li

For a positive integer $m$ let ${\Omega }_m=\{0,1,\cdots ,m\}$ and \begin{align*} \mathcal B_2(m)=&\left \{q\in(1,m+1]: \text{$\exists x\in [0,m/(q-1)]$ has exactly }\right. \\ &\left…