On Periodic Points of the Order of Appearance in the Fibonacci Sequence

Eva Trojovská
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Eva Trojovská: Department of Mathematics, Faculty of Science, University of Hradec Králové, 50003 Hradec Králové, Czech Republic

Mathematics, 2020, vol. 8, issue 5, 1-8

Abstract: Let ( F n ) n ≥ 0 be the Fibonacci sequence. The order of appearance z ( n ) of an integer n ≥ 1 is defined by z ( n ) = min { k ≥ 1 : n ? F k } . Marques, and Somer and K?ížek proved that all fixed points of the function z ( n ) have the form n = 5 k or 12 · 5 k . In this paper, we shall prove that z ( n ) does not have any k -periodic points, for k ≥ 2 .

Keywords: diophantine equation; Fibonacci number; order of appearance; p-adic valuation; arithmetic dynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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