On Fixed Points of Iterations Between the Order of Appearance and the Euler Totient Function

Štěpán Hubálovský and Eva Trojovská
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Štěpán Hubálovský: Department of Applied Cybernetics, Faculty of Science, University of Hradec Králové, 50003 Hradec Králové, Czech Republic
Eva Trojovská: Department of Mathematics, Faculty of Science, University of Hradec Králové, 50003 Hradec Králové, Czech Republic

Mathematics, 2020, vol. 8, issue 10, 1-5

Abstract: Let F n be the n th Fibonacci number. The order of appearance z ( n ) of a natural number n is defined as the smallest positive integer k such that F k ≡ 0 ( mod n ) . In this paper, we shall find all positive solutions of the Diophantine equation z ( φ ( n ) ) = n , where φ is the Euler totient function.

Keywords: Fibonacci numbers; order of appearance; Euler totient function; fixed points; Diophantine equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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