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García, Victor C.; Luca, Florian; Mejía Huguet, V. Janitzio

On sums of Fibonacci numbers modulo \(p\). (English) Zbl 1238.11011

Bull. Aust. Math. Soc. 83, No. 3, 413-419 (2011).
The authors prove that the set of primes \(p\) such that every residue class modulo \(p\) is a sum of 32 Fibonacci numbers is of relative asymptotic density 1.
Reviewer: Florin Nicolae (Berlin)

Cited in 2 Documents

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11B50 Sequences (mod \(m\))

Keywords:

Fibonacci numbers
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References:

[1] DOI: 10.4007/annals.2008.168.367 · Zbl 1181.11058 · doi:10.4007/annals.2008.168.367
[2] Erdos, Number Theory (Ottawa, ON, 1996) pp 87– (1999)
[3] Glibichuk, Mat. Zametki 79 pp 384– (2006) · doi:10.4213/mzm2708
[4] Luca, Fibonacci Quart. 45 pp 98– (2007)
[5] DOI: 10.4064/aa119-2-2 · Zbl 1080.11059 · doi:10.4064/aa119-2-2
[6] DOI: 10.1006/jnth.1996.0044 · Zbl 0847.11049 · doi:10.1006/jnth.1996.0044
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