Length of period simple continued fraction expansion of √d

Dean Robert Hickerson

Vol. 46 (1973), No. 2, 429–432

DOI: 10.2140/pjm.1973.46.429

Abstract

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

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

Mathematical Subject Classification

Primary: 10F20

Milestones

Received: 28 April 1972

Published: 1 June 1973