On length of the period of the continued fraction of nvd

被引：0
|
作者：
Gawron, Filip [1 ]
Kobos, Tomasz [1 ]
机构：
[1] Jagiellonian Univ, Fac Math & Comp Sci, Lojasiewicza 6, PL-30348 Krakow, Poland
来源：
INTERNATIONAL JOURNAL OF NUMBER THEORY | 2023年 / 19卷 / 09期
关键词：
Continued fraction; period; quadratic irrational; Pell equation; Euclidean algorithm;
D O I：
10.1142/S1793042123501014
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For a given quadratic irrational a, let us denote by D(a) the length of the periodic part of the continued fraction expansion of a. We prove that for every positive integer d, which is not a perfect square, there are infinitely many even integers k = 1, for which v the equality D(nvd) = k holds for infinitely many integers n = 1.
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页码：2089 / 2099
页数：11
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