Quotients of Fibonacci Numbers

Quotients of Fibonacci Numbers

There have been many articles in the MONTHLY on quotient sets over the years. We take a first step here into the p-adic setting, which we hope will spur further research. We show that the set of quotients of nonzero Fibonacci numbers is dense in the p-adic numbers for every prime p.

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Veröffentlicht in:The American mathematical monthly 2016-12, Vol.123 (10), p.1039-1044
Hauptverfasser: Garcia, Stephan Ramon, Luca, Florian
Format: Artikel
Sprache:eng
Schlagworte:
Fibonacci numbers
Mathematical analysis
Numbers
Prime numbers
Quotients
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Zusammenfassung:There have been many articles in the MONTHLY on quotient sets over the years. We take a first step here into the p-adic setting, which we hope will spur further research. We show that the set of quotients of nonzero Fibonacci numbers is dense in the p-adic numbers for every prime p.
ISSN:0002-9890
1930-0972
DOI:10.4169/amer.math.monthly.123.10.1039