Cover Image

Sum of consecutive powers as a perfect power

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Koutsianas, Angelos, Tzanakis, Nikos
Format:	Preprint
Published:	2026
Subjects:	Number Theory 1D41, 11G10
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Darmon's Program: A survey
by: Chen, Imin, et al.
Published: (2025)

The generalized Fermat equation $Ax^2 + By^r = Cz^p$ and applications
by: García, Pedro-José Cazorla, et al.
Published: (2026)

A modular approach to Fermat equations of signature $(p,p,5)$ using Frey hyperelliptic curves
by: Chen, Imin, et al.
Published: (2022)

Perfect powers among Jacobsthal numbers
by: Virbalas, Paulius
Published: (2026)

Non-trivial Integer Solutions of $x^r+y^r=Dz^p$
by: Kara, Yasemin, et al.
Published: (2024)

On $k$-th power Diophantine triples of the form $\{a^k, b, c\}$
by: Fuchs, Clemens, et al.
Published: (2026)

On the generalized Fermat equation $x^{13} + y^{13} = z^n$
by: Best, Alex J., et al.
Published: (2025)

Selmer ranks in twists of CM abelian varieties
by: Shu, Jie
Published: (2025)

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

Local-global principle for 11-isogenies of elliptic curves is true over quadratic fields
by: Gajović, Stevan, et al.
Published: (2025)

On the conductor of a family of Frey hyperelliptic curves
by: García, Pedro-José Cazorla, et al.
Published: (2025)

A multi-Frey approach to Fermat equations of signature $(r,r,p)$
by: Billerey, Nicolas, et al.
Published: (2017)

A survey on the generalized Fermat equation of various signatures over totally real fields
by: Sahoo, Satyabrat
Published: (2025)

On Sum-Free Functions
by: Ebeling, Alyssa, et al.
Published: (2024)

A note on conductors of Frey representations at $2$
by: Chen, Imin, et al.
Published: (2025)

Frobenius sign separation for abelian varieties
by: Bucur, Alina, et al.
Published: (2023)

On a Conjecture About the Sum-Freedom of the Binary Multiplicative Inverse Function
by: Hou, Xiang-dong, et al.
Published: (2025)

Solving equations of signature $(p,p,2)$ with coefficients over number fields
by: Cakti, Begum Gulsah, et al.
Published: (2026)

Solving Fermat-type equations over quadratic fields
by: Cakti, Begum Gulsah
Published: (2025)

Generalised Fermat equation: a survey of solved cases
by: Ratcliffe, Ashleigh, et al.
Published: (2024)

Generalized fruit Diophantine equation and super elliptic curves
by: Banerjee, Kalyan, et al.
Published: (2026)

The diophantine equation $\left(2^{k}-1\right)\left(3^{k}-1\right)=x^{n}$
by: He, Bo, et al.
Published: (2025)

On Darmon's program for the generalized Fermat equation, I
by: Billerey, Nicolas, et al.
Published: (2022)

Fermat descent
by: Arango-Piñeros, Santiago
Published: (2025)

On Darmon's program for the Generalized Fermat equation, II
by: Billerey, Nicolas, et al.
Published: (2023)

The sufficient conditions for insolvability of some Diophantine equations of $n$-th degree
by: Samsonadze, Eteri
Published: (2025)

Counting rational points on smooth hypersurfaces with high degree
by: Verzobio, Matteo
Published: (2025)

Solution of the Diophantine equation $x^2 + p^k=y^n$
by: Ghosh, Arkabrata
Published: (2024)

On a nonlinear Diophantine equation with powers of three consecutive $k$--Lucas Numbers
by: Batte, Herbert, et al.
Published: (2024)

Non-trivial Solutions of $Aa^p+Bb^p=Cc^3$ over Number Fields
by: Kara, Yasemin, et al.
Published: (2025)

Near-squares in binary recurrence sequences
by: Tzanakis, Nikos, et al.
Published: (2021)

Arithmetic Bias in Mersenne Prime Exponents and the Divisor Structure of $p-1$
by: Dominguez, Jesus
Published: (2026)

Genus-One Fibrations and the Jacobian of Linear Slices in the Quintic Equal-Sum Problem
by: Asiryan, Valery
Published: (2025)

On the difference between perfect powers and integral $S$-units
by: Bugeaud, Yann
Published: (2026)

On 7-adic Galois representations for elliptic curves over $\mathbb{Q}$
by: Furio, Lorenzo, et al.
Published: (2025)

The modular approach to Diophantine equations over totally real fields
by: Khawaja, Maleeha, et al.
Published: (2024)

Diophantine tuples and product sets in shifted powers
by: Croot, Ernie, et al.
Published: (2025)

(Algebraic) $ p $-adic Artin formalism of twisted triple product Galois representations over real quadratic fields
by: Das, Bhargab, et al.
Published: (2025)

Structure and paucity in affine diagonal systems, I
by: Brandes, Julia, et al.
Published: (2026)

The exceptional set in the abc conjecture
by: Bernert, Christian
Published: (2025)