Pure quintic fields which can be defined by a trinomial X5 + aX + b or X5 + aX2 + b, where a and b are nonzero rational numbers, are characterized. Using this characterization it is shown that the only pure quintic field Q(p1/5) (p a prime) which can be defined by a trinomial is Q(21/5) = Q(θ), where θ is the unique real root of x5 + 100x2 + 1000 = 0.

Additional Metadata
Keywords Pure quintic fields, Solvable quintic trinomials
Journal Rocky Mountain Journal of Mathematics
Spearman, B.K. (Blair K.), & Williams, K.S. (2000). Pure quintic fields defined by trinomials. Rocky Mountain Journal of Mathematics, 30(1), 371–391.