Vol. 46, No. 2, 1973

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ISSN: 0030-8730
Length of period simple continued fraction expansion of d

Dean Robert Hickerson

Vol. 46 (1973), No. 2, 429–432
Abstract

In this article, the length, p(d), of the period of the simple continued fraction (s.c.f.) for √d- is discussed, where d is a positive integer, not a perfect square. In particular, it is shown that

p(d) < d1∕2+log2∕loglogd+O(logloglogd∕(loglogd)2).

In addition, some properties of the complete quotients of the s.c.f. expansion of √-
d are developed.

Mathematical Subject Classification
Primary: 10F20
Milestones
Received: 28 April 1972
Published: 1 June 1973
Authors
Dean Robert Hickerson