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On generalised Fibonaccian and Lucasian numbers

Published online by Cambridge University Press:  01 August 2016

Peter Hilton  and
Jean Pedersen
Peter Hilton
Affiliation:
Department of Mathematical Sciences, State University of New York at Binghamton, Binghamton, New York 13902-6000USA e-mail: jpedersen@scu.edu
Jean Pedersen
Affiliation:
Department of Mathematics & CS, Santa Clara University, Santa Clara, California 95120-0290USA
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Extract

In [1, Chapter 3, Section 2], we collected together results we had previously obtained relating to the question of which positive integers m were Lucasian, that is, factors of some Lucas number Ln. We pointed out that the behaviors of odd and even numbers m were quite different. Thus, for example, 2 and 4 are both Lucasian but 8 is not; for the sequence of residue classes mod 8 of the Lucas numbers, n ⩾ 0, reads

and thus does not contain the residue class 0*. On the other hand, it is a striking fact that, if the odd number s is Lucasian, then so are all of its positive powers.

Type
Articles
Information
The Mathematical Gazette , Volume 90 , Issue 518 , July 2006 , pp. 215 - 222
Copyright
Copyright © The Mathematical Association 2006

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References

1. Hilton, Peter Holton, Derek and Pedersen, Jean Mathematical vistas – from a room with many mirrors, Undergraduate Texts in Mathematics, Springer-Verlag NY (2002).Google Scholar