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Ankeny, Artin and Chowla  proved a congruence relation among the class number, the fundamental unit of real quadratic fields, and the Bernoulli numbers. Our aim of this paper is to prove similar congruence relations for pure cubic fields. For this purpose, we use the Hurwitz numbers associated with the elliptic curve defined by y2 = 4x3 — 1 instead of the Bernoulli numbers (§ 3).doi:10.1017/s0027763000021164 fatcat:x5cberpv3jcb7dovhhadaiio4u