Salem number is a real algebraic integer $\alpha>1$ whose algebraic conjugates all lie in the unit disk $\{\,z\in\mathbb{C} \,\big|\, |z|\leq 1\,\}$ with at least one on the unit circle $\{\,z\in\mathbb{C}\,\big|\,|z|= 1\,\}$ .

Powers of a Salem number are everywhere dense modulo $1$ , but are not uniformly distributed modulo $1$ .

The smallest known Salem number is the largest positive root of \begin{equation*} \alpha^{10}+\alpha^9-\alpha^7-\alpha^6-\alpha^5-\alpha^4-\alpha^3+\alpha+1=0. \end{equation*}