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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: [email protected])
FLORIAN LUCA*
Affiliation:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, C.P. 58089, Morelia, Michoacán, México (email: [email protected])
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: [email protected])
*
✉For correspondence; e-mail: [email protected]
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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

[1]Erdős, P. and Murty, M. R., ‘On the order of a (mod p)’, in: Number Theory (Ottawa, ON, 1996), CRM Proceedings and Lecture Notes, 19 (American Mathematical Society, Providence, RI, 1999), pp. 87–97.Google Scholar
[2]Ford, K., ‘The distribution of integers with a divisor in a given interval’, Ann. of Math. (2) 168 (2008), 367–433.CrossRefGoogle Scholar
[3]Glibichuk, A., ‘Combinatorial properties of sets of residues modulo a prime and the Erdős–Graham problem’, Mat. Zametki 79 (2006), 384–395; English translation, Math. Notes 79(3–4) (2006), 356–365.Google Scholar
[4]Kurlberg, P. and Pomerance, C., ‘On the periods of the linear congruential and power generators’, Acta Arith. 119 (2005), 149–169.CrossRefGoogle Scholar
[5]Luca, F. and Szalay, L., ‘Fibonacci numbers of the form p a±p b+1’, Fibonacci Quart. 45 (2007), 98–103.Google Scholar
[6]Pappalardi, F., ‘On the order of finitely generated subgroups of ℚ* (mod p) and divisors of p−1’, J. Number Theory 57 (1996), 207–222.CrossRefGoogle Scholar