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ON SUMS OF FIBONACCI NUMBERS MODULO p

Part of: Sequences and sets

Published online by Cambridge University Press:  17 November 2010

VICTOR C. GARCÍA ,
FLORIAN LUCA  and
V. JANITZIO MEJÍA HUGUET
VICTOR C. GARCÍA
Affiliation:
Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana-Azcapotzalco, Av. San Pablo #180, Col. Reynosa Tamaulipas, Azcapotzalco, C.P. 02200, México DF, México (email: vc.garci@gmail.com)
FLORIAN LUCA*
Affiliation:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, C.P. 58089, Morelia, Michoacán, México (email: fluca@matmor.unam.mx)
V. JANITZIO MEJÍA HUGUET
Affiliation:
Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana-Azcapotzalco, Av. San Pablo #180, Col. Reynosa Tamaulipas, Azcapotzalco, C.P. 02200, México DF, México (email: vjanitzio@gmail.com)
*
✉For correspondence; e-mail: fluca@matmor.unam.mx
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Abstract

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Here, we show that for most primes p, every residue class modulo p can be represented as a sum of 32 Fibonacci numbers.

Keywords

Fibonacci numbers

MSC classification

Secondary: 11B39: Fibonacci and Lucas numbers and polynomials and generalizations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 83 , Issue 3 , June 2011 , pp. 413 - 419
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

During the preparation of this paper, V.C.G. was supported by Grant UAM-A 2232508, F.L. was supported in part by Grants SEP-CONACyT 79685 and PAPIIT 100508, and V.J.M.H. was supported in part by Grant UAM-A 2232508 and a postdoctoral position at the IFM of UMSNH.

References

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