Cover Image

Diophantine equations over the generalized Fibonacci sequences: exploring sums of powers

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Alvarenga, Roberto, Chaves, Ana Paula, Ramos, Maria Eduarda, Silva, Matheus, Sosa, Marcos
Format:	Preprint
Published:	2025
Subjects:	Number Theory
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Fibonacci Numbers as Sums of Consecutive Terms in $k$-Generalized Fibonacci Sequence
by: Alvarenga, Roberto, et al.
Published: (2025)

$Ω$-bounds for the partial sums of some modified Dirichlet characters II
by: Aymone, Marco, et al.
Published: (2025)

The inverse of the (alternating) infinite sum of the reciprocal of the weighted sum for generalized Fibonacci sub-sequences
by: Wan, Yongkang, et al.
Published: (2025)

On Diophantine equations with Fibonacci and Lucas sequences associated to Hardy-Ramanujan problem
by: Daşdemir, Ahmet
Published: (2023)

Limiting density of the Fibonacci sequence modulo powers of a prime
by: Bragman, Nicholas, et al.
Published: (2022)

Representing integers as sums of mixed powers of primes
by: Andrade, Geovane Matheus Lemes, et al.
Published: (2025)

Computing bounded solutions to linear Diophantine equations with the sum of divisors
by: Alekseyev, Max A.
Published: (2026)

The asymptotic estimation for two classes of generalized Fibonacci sub-sequences
by: Wan, Yongkang, et al.
Published: (2025)

Fibonacci sequences in $\mathbb F_p$
by: Aka, Menny
Published: (2025)

Kac--Moody Fibonacci sequences
by: Carbone, Lisa, et al.
Published: (2026)

A Pair of Diophantine Equations Involving the Fibonacci Numbers
by: Chen, Xuyuan, et al.
Published: (2024)

Diophantine approximation with mixed powers of Piatetski-Shapiro primes
by: Dimitrov, S. I.
Published: (2025)

The exceptional set for Diophantine inequality with mixed powers of primes
by: Fu, Yu, et al.
Published: (2026)

Diophantine equations with sum of cubes and cube of sum
by: Dobrescu, Bogdan A., et al.
Published: (2020)

Diophantine stability for curves over finite fields
by: Bars, Francesc, et al.
Published: (2024)

On Transformation properties of hypergeometric motives and Diophantine equations
by: Pacetti, Ariel
Published: (2025)

Fibonacci Numbers and Vieta Jumping for a Rational Diophantine Equation
by: Miller, Steven J., et al.
Published: (2026)

Asymptotics for partitions over the Fibonacci numbers and related sequences
by: Coons, Michael, et al.
Published: (2023)

Diophantine equations involving powers of factorials
by: Novaković, Saša
Published: (2025)

Reverse Engineered Diophantine Equations over $\mathbb{Q}$
by: Santicola, Katerina
Published: (2022)

On sums of unequal powers of primes and powers of 2
by: Liu, Yuhui
Published: (2023)

Finiteness of solutions to linear Diophantine equations on Piatetski-Shapiro sequences
by: Saito, Kota
Published: (2023)

Product of powers of distinct primes as sums of Fibonacci numbers
by: Batte, Herbert, et al.
Published: (2026)

Fibonacci along even powers is (almost) realizable
by: Moss, Patrick, et al.
Published: (2020)

Decidability of multiplicative matrix equations and related Diophantine problems
by: Heintze, Sebastian, et al.
Published: (2025)

On general divisor functions over Piatetski-Shapiro sequences
by: Zhang, Wei
Published: (2023)

Liminf-results for sums with Kronecker sequence
by: Chebotarenko, Artem
Published: (2025)

S-unit equations in modules and linear-exponential Diophantine equations
by: Dong, Ruiwen, et al.
Published: (2025)

A Diophantine inequality involving different powers of primes of the form $[n^c]$
by: Dimitrov, S. I.
Published: (2026)

On Iwasawa theory of abelian varieties over $\mathbb{Z}_p^2$-extension with applications to Diophantine stability and integally Diophantine extensions
by: Lim, Meng Fai
Published: (2026)

On some ternary Diophantine equations of Signature $(p,p,k)$
by: Noubissie, Armand, et al.
Published: (2025)

Cotangent power sums and character coordinates
by: Girstmair, Kurt
Published: (2025)

On the sum of fifth powers in arithmetic progression
by: Torcomian, Lucas Villagra
Published: (2024)

Hecke eigenspaces for the projective line
by: Alvarenga, Roberto, et al.
Published: (2023)

A note on the power sums of the number of Fibonacci partitions
by: Sanna, Carlo
Published: (2023)

Powerful Fibonacci polynomials over finite fields
by: Bates, Graeme, et al.
Published: (2026)

The equidistribution of Elliptic Dedekind sums and generalized Selberg-Kloosterman sums
by: Klinger-Logan, Kim, et al.
Published: (2024)

The image of the generalized Dedekind sum
by: Knight, Evelyne S., et al.
Published: (2025)

A Pair of Diophantine Equations and Fibonacci-Like Sequences
by: Chu, Hung Viet, et al.
Published: (2025)

Matrix Kloosterman sums modulo prime powers
by: Erdélyi, Márton, et al.
Published: (2022)