 Some Remarks on the Distribution of Second Order Recurrences and a Related Group StructureJohn R. Burke A chapter in Applications of Fibonacci Numbers, 1996, pp 47-52 from Springer Abstract: Abstract The distribution properties of the Fibonacci numbers have been closely examined by several authors and from several different viewpoints. One of the earliest results, due to Kuipers and Shiue [5], established that the Fibonacci numbers are uniformly distributed mod p (u.d. mod p) if and only if p = 5. They conjectured that the Fibonacci numbers were u.d. mod for each h ⪰ 1. Niederreiter established the conjecture in [9]. Kuipers and Shiue went on to consider the distribution of general second order recurrences [6]. In 1975, Webb and Long (W-L) characterized all second order recurrences which were u.d. mod ph [13]. (Similar results were established independently by Bumby [1] and Nathanson [8]. See also [2, 7, 10, 11].) In the following a relationship between u.d. mod p second order recurrences (when they exist) and those sequences satisfying the same recurrence relation but are not u.d. mod p will be established. It will be shown that there is a rather simple group structure in which the u.d. mod p sequences and those that are not form the elements. There is also a related result that we will obtain about the independence mod p of certain second order linear recurrences. Date: 1996 There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-0223-7_4 Ordering information: This item can be ordered from DOI: 10.1007/978-94-009-0223-7_4 Access Statistics for this chapter More chapters in Springer Books from Springer |
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