Periodic solutions to some difference equations over the integers

被引：4

作者：

Greene, John ^{[1
]}

Niedzielski, Katherine ^{[1
]}

机构：

[1] Univ Minnesota, Dept Math & Stat, Duluth, MN 55812 USA

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2010年 / 16卷 / 04期

关键词：

difference equation; periodic solutions; Fibonacci identities; Lucas numbers;

D O I：

10.1080/10236190802395172

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate periodic integer solutions {a(n)} to a(n) = {r(a(n-1) + a(n-2)), if r(a(n-1) + a(n-2)) is an interger, a(n-1) + a(n-2), otherwise, where r is a rational number. We show that solutions can only exist, if -1 <= r <= 1/2 and we give several infinite families of rs, for which the above recurrence has periodic solutions in the integers.

引用

页码：321 / 346

页数：26

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