COMPARISON OF THE LENGTHS OF THE CONTINUED FRACTIONS OF ROOT-D AND 1/2(1+ROOT-D)

被引：10

作者：

WILLIAMS, KS ^{[1
]}

BUCK, N ^{[1
]}

机构：

[1] COLL NEW CALEDONIA,DEPT MATH,PRINCE GEORGE V2N 1P8,BC,CANADA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1994年 / 120卷 / 04期

关键词：

CONTINUED FRACTIONS;

D O I：

10.2307/2160208

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let D denote a positive nonsquare integer such that D = 1 (mod 4). Let l(square-root D) (resp. l(1 + square-root D))) denote the length of the period of the continued fraction expansion of square-root D (resp. 1/2(1 + square-root D)). Recently Ishii, Kaplan, and Williams (On Eisenstein's problem, Acta Arith. 54 (1990), 323-345) established inequalities between l(square-root D) and l(1/2(1 + square-root D)). In this note it is shown that these inequalities are best possible in a strong sense.

引用

页码：995 / 1002

页数：8