  Let $m\neq0,\pm1$ and $n\geq 2$ be integers. The ring of algebraic integers
of the pure fields of type $\mathbb{Q}(\sqrt[n]{m})$ is explicitly known for
$n=2,3,4$. It is well known that for $n=2$, an integral basis of the pure
quadratic fields can be given parametrically, by using the remainder of the
square-free part of $m$ modulo 4. Such characterisation of an integral basis
also exists for cubic and quartic pure fields, but for higher degree pure
fields there are only results for special cases.\\ In this paper we explicitly
give an integral basis of the field $\mathbb{Q}(\sqrt[n]{m})$, where
$m\neq\pm1$ is square-free. Furthermore, we show that similarly to the
quadratic case, an integral basis of $\mathbb{Q}(\sqrt[n]{m})$ is repeating
periodically in $m$ with period length depending on $n$.
