On prime factors of the sum of two k-Fibonacci numbers
| Autor: | Florian Luca, Carlos Alexis Gómez Ruiz |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Algebra and Number Theory
Fibonacci number Almost prime Computer Science::Information Retrieval 010102 general mathematics Astrophysics::Instrumentation and Methods for Astrophysics Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) 010103 numerical & computational mathematics 01 natural sciences Probable prime Prime k-tuple Combinatorics Prime factor Computer Science::General Literature 0101 mathematics Prime power Mathematics Sphenic number Primorial |
| Zdroj: | International Journal of Number Theory |
| ISSN: | 1793-7310 1793-0421 |
| DOI: | 10.1142/s1793042118500720 |
| Popis: | We consider for integers [Formula: see text] the [Formula: see text]-generalized Fibonacci sequences [Formula: see text], whose first [Formula: see text] terms are [Formula: see text] and each term afterwards is the sum of the preceding [Formula: see text] terms. We give a lower bound for the largest prime factor of the sum of two terms in [Formula: see text]. As a consequence of our main result, for every fixed finite set of primes [Formula: see text], there are only finitely many positive integers [Formula: see text] and [Formula: see text]-integers which are a non-trivial sum of two [Formula: see text]-Fibonacci numbers, and all these are effectively computable. |
| Databáze: | OpenAIRE |
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