Even and odd periods in continued fractions of square roots

Rippon, Philip and Taylor, Harold (2004). Even and odd periods in continued fractions of square roots. Fibonacci Quarterly, 42(2) pp. 170–180.

URL:	http://www.engineering.sdstate.edu/~fib/fibpreviou...
Google Scholar:	Look up in Google Scholar

Abstract

The continued fraction for $\sqrt{N}$ , where $N$ is a positive integer, has the periodic form
$\sqrt{N}=[a_0,\overline{a_1,a_2,\ldots, a_l}\,],$
where $a_1,a_2,\ldots,a_{l-1}$ is a palindrome and $a_l=2a_0$ . The period $l=l(N)$ is assumed to be
of minimal length. We give several new results concerning the intriguing question: How can we distinguish between those integers $N$ for which $l(N)$ is even and
those for which $l(N)$ is odd?

Item Type:	Article
ISSN:	0015-0517
Extra Information:	Some of the symbols may not have transferred correctly into this bibliographic record.
Keywords:	continued fraction; square root; period; Euler-Muir theorem.
Academic Unit/School:	Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID:	3631
Depositing User:	Philip Rippon
Date Deposited:	30 Jun 2006
Last Modified:	04 Oct 2016 09:50
URI:	http://oro.open.ac.uk/id/eprint/3631
Share this page:

▼ Automated document suggestions from open access sources

Actions (login may be required)

Policies | Disclaimer