The 2-adic valuation of generalized Fibonacci sequences with an application to certain Diophantine equations
Copyright policy )The 2-adic valuation of generalized Fibonacci sequences with an application to certain Diophantine equations
In this paper we focus on finding all the factorials expressible as a product of a fixed number of $2k$-nacci numbers with $k \geq 2$. We derive the 2-adic valuation of the $2k$-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.
10 pages
- Polish Academy of Sciences Poland
- Institute of Mathematics Poland
- Jagiellonian University Poland
factorials, Mathematics - Number Theory, Diophantine equations, Binomial coefficients; factorials; \(q\)-identities, \(p\)-adic valuation, FOS: Mathematics, Fibonacci and Lucas numbers and polynomials and generalizations, Number Theory (math.NT), 11B39, 11B65, 11D99, generalized Fibonacci sequences
factorials, Mathematics - Number Theory, Diophantine equations, Binomial coefficients; factorials; \(q\)-identities, \(p\)-adic valuation, FOS: Mathematics, Fibonacci and Lucas numbers and polynomials and generalizations, Number Theory (math.NT), 11B39, 11B65, 11D99, generalized Fibonacci sequences
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