An upper bound for the period of the simple continued fraction for

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

Vol. 67 (1976), No. 2, 525–536

DOI: 10.2140/pjm.1976.67.525

Abstract

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

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