Abstract
That the ratio F kn /F n , where F n is the n-th Fibonacci number, is integral is a well-known fact. Define
for all positive integral values of k and n.
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References
Batut, C, Bernardi, D., Cohen, H. and Olivier, M. “The Software Package PARI.” UFR de Mathématiques et Informatique, Université Bordeaux I. Private communication.
Freitag, H. T. and Filipponi, P. “On the Representation of Integral Sequences {F n /d} and {L n /d} as Sums of Fibonacci Numbers and as Sums of Lucas Numbers.” Applications of Fibonacci Numbers, Volume 2. Edited by A. N. Philippou, A. F. Horadam and G. E. Bergum. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1988: pp. 97–112.
Freitag, H. T. “On the Representation of {F kn /F n }, {F kn /L n}, {L kn /F n } and {L kn /L n } as Zeckendorf Sums.” Applications of Fibonacci Numbers, Volume 3. Edited by G. E. Bergum, A. N. Philippou and A. F. Horadam. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1990: pp. 107–114.
Hoggatt, V. E., Jr. Fibonacci and Lucas Numbers. Boston: Houghton Mifflin, 1969.
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© 1993 Springer Science+Business Media Dordrecht
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Filipponi, P., Freitag, H.T. (1993). The Zeckendorf Representation of {F kn /F n }. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2058-6_20
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