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The 2-adic valuation of generalized Fibonacci sequences with an application to certain Diophantine equations.
- Source :
-
Journal of Number Theory . Nov2017, Vol. 180, p730-742. 13p. - Publication Year :
- 2017
-
Abstract
- In this paper we focus on finding all the factorials expressible as a product of a fixed number of 2 k -nacci numbers with k ≥ 2 . We derive the 2-adic valuation of the 2 k -nacci sequence and use it to establish bounds on the solutions of the initial equation. In addition, we specify a more general family of sequences, for which we can perform a similar procedure. We also investigate a possible connection of these results with p -regular sequences. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FIBONACCI sequence
*NUMBER theory
*ALGEBRA
*ARITHMETIC
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 180
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 124357037
- Full Text :
- https://doi.org/10.1016/j.jnt.2017.06.008