Closed formulae for certain Fermat-Pell equations

被引：0
|
作者：
Szechtman, Fernando [1 ]
机构：
[1] Univ Regina, Dept Math & Stat, Regina, SK S4S 0A2, Canada
来源：
COMMUNICATIONS IN ALGEBRA | 2022年 / 50卷 / 02期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Continued fraction; Fermat-Pell equation;
D O I：
10.1080/00927872.2021.1964028
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given positive integers j, k, with j >= 2, we show that there are positive integers d, e such that root d has continued fraction expansion root d = [e, k, ..., k, 2e], with period j, if and only if k is even or 3 inverted iota j, in which case we give closed formulae to find all such d, e as well as the smallest solution in positive integers to the Fermat-Pell equation X-2 - dY(2) = (-1)(1.)
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页码：661 / 667
页数：7
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