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.

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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:	Journal 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/Department:	Mathematics, Computing and Technology > Mathematics and Statistics
Item ID:	3631
Depositing User:	Philip Rippon
Date Deposited:	30 Jun 2006
Last Modified:	02 Dec 2010 19:50
URI:	http://oro.open.ac.uk/id/eprint/3631
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