Vol. 67, No. 2, 1976

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ISSN: 0030-8730
An upper bound for the period of the simple continued fraction for √D-

Ralph Gordon Stanton, C. Sudler and Hugh C. Williams

Vol. 67 (1976), No. 2, 525–536
Abstract

Let p(D) denote the length of the period of the simple continued-fraction expansion of √D-- where D is a positive non-square integer. In this paper, it is shown that

p(D ) < 0.72D1 ∕2 logD

for all squarefree D > 7, and an estimate for p(D) is given when D is not squarefree.

Mathematical Subject Classification
Primary: 10A30, 10A30
Milestones
Received: 10 June 1975
Revised: 19 July 1976
Published: 1 December 1976
Authors
Ralph Gordon Stanton
C. Sudler
Hugh C. Williams
Department of Mathematics & Statistics
University of Calgary
2500 University Drive NW
Calgary AB T2N 1N4
Canada