On the fundamental unit of a purely cubic field

Ronald Joel Rudman

Vol. 46 (1973), No. 1, 253–256

DOI: 10.2140/pjm.1973.46.253

Abstract

Let a = D⁸ + d, where a,D,d are rational integers with D,a > 0,|d| > 1, and d|3D² It is proved that the fundamental unit of the field Q(ω), where ω = , is (ω − D)⁸∕d with only six exceptions.

Mathematical Subject Classification

Primary: 12A45

Milestones

Received: 28 February 1972

Published: 1 May 1973