Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 4 / 12H / a / Solution

Liouville approximation theorem states that if $\alpha$ is a real algebraic number of degree $d\ge 2$, then there is a constant $c(\alpha )>0$ such thatfor every rational $p/q$ with $q>0$. The strict inequality may be replaced by a non-strict one after changing the constant.