Normal integral bases of Lehmer's cyclic quintic fields (Q6624959)

Let \(K_n\) be the cyclic field generated by a root of the polynomial\N\[\NP_n(x) = x^5+n^2x^4-(2n^2+6n^2+10n+10)x^3+(n^4+5n^3+11n^2+5n+5)x^2\N\]\N\[\N+(n^3+4n^2+10n+10)x+1,\N\]\Nintroduced by \textit{E. Lehmer} [Math. Comput. 50, No. 182, 535--541 (1988; Zbl 0652.12004)]. The authors construct an integral basis for \(K_n\) and use it in in the case \(5|n\) to provide a normal integral basis (the Hilbert-Speiser theorem implies that in the case \(5\nmid n\) there is no normal integral basis).