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Prime factors in generalised Fibonacci sequences - a question posed by Gill Hatch*

Published online by Cambridge University Press:  01 August 2016

R. P. Burn*
Affiliation:
Sunnyside, Barrack Road, Exeter EX2 6AB, R.P.Burn@exeter.ac.uk

Extract

Those who enjoy number patterns will no doubt have had many hours of pleasure exploring the Fibonacci sequence to various moduli, and especially in recognising the regularity with which various prime factors occur in thesequence (see [1]). Gill Hatch’s question is whether the occurrence of prime factors in generalised Fibonacci sequences is similarly predictable. Generalised Fibonacci sequences (Gn), abbreviated to GF sequences, are sequences of positive integers derived from the recurrence relation tn + 2 = tn + 1 + tn. In the case of the Fibonacci sequence (Fn), the first two terms are 1 and 1.

Type
Articles
Copyright
Copyright © The Mathematical Association 2003

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Footnotes

*

Article submitted on the occasion of her retirement.

References

1. Marshall, A. G. Fibonacci, modulo n , Mathematics Teaching, 46 (1969) p. 29.Google Scholar
2. Hardy, G. H. and Wright, E. M. An introduction to the theory of numbers (4th edn), Oxford University Press (1975).Google Scholar