Periodic solutions to some difference equations over the integers

John R Greene; Kate Niedzielski

doi:10.1080/10236190802395172

Periodic solutions to some difference equations over the integers

John R Greene
, Kate Niedzielski

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this paper, we investigate periodic integer solutions {a_n} to 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.

Original language	English (US)
Pages (from-to)	321-346
Number of pages	26
Journal	Journal of Difference Equations and Applications
Volume	16
Issue number	4
DOIs	https://doi.org/10.1080/10236190802395172
State	Published - Apr 2010

Keywords

Difference equation
Fibonacci identities
Lucas numbers
Periodic solutions

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10.1080/10236190802395172

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title = "Periodic solutions to some difference equations over the integers",

abstract = "In this paper, we investigate periodic integer solutions \{an\} to 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.",

keywords = "Difference equation, Fibonacci identities, Lucas numbers, Periodic solutions",

author = "Greene, \{John R\} and Kate Niedzielski",

year = "2010",

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language = "English (US)",

volume = "16",

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journal = "Journal of Difference Equations and Applications",

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AU - Niedzielski, Kate

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AB - In this paper, we investigate periodic integer solutions {an} to 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.

KW - Difference equation

KW - Fibonacci identities

KW - Lucas numbers

KW - Periodic solutions

UR - https://www.scopus.com/pages/publications/77951180578

UR - https://www.scopus.com/pages/publications/77951180578#tab=citedBy

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DO - 10.1080/10236190802395172

M3 - Article

AN - SCOPUS:77951180578

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EP - 346

JO - Journal of Difference Equations and Applications

JF - Journal of Difference Equations and Applications

IS - 4

ER -

Periodic solutions to some difference equations over the integers

Abstract

Keywords

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