Pure quintic fields defined by trinomials (Q5928681)

The authors give a characterization of pure quintic fields which can be generated by a root of a trinomial. It turns out that there is a one-parameter family of such fields generated by a root of \(X^5+aX+b\) (\(ab\neq 0\)) and only one field, namely \(\mathbb{Q}(\root 5\of 2)\), which can be generated by a root of a polynomial of the form \(X^5+aX^2+b\) with \(ab\neq 0\).