Cover Image

Circularity in Finite Fields and Solutions of the Equations $\boldsymbol{x^{m}+y^{m}-z^{m}=1}$

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Ke, Wen-Fong, Kiechle, Hubert
Format:	Preprint
Published:	2023
Subjects:	Number Theory Combinatorics
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Overlaps in Field Generated Circular Planar Nearrings
by: Ke, Wen-Fong, et al.
Published: (2023)

Rainbow Numbers for the Generalized Schur Equation $x_1 + x_2 + \cdots + x_{m-1} = x_m$
by: Budden, Mark, et al.
Published: (2024)

An Analytical Exploration of the Erdös-Moser Equation $ \sum_{i=1}^{m-1} i^k = m^k $ Using Approximation Methods
by: Lambard, Guillaume
Published: (2024)

Proof of a conjecture of Garvan and Jennings-Shaffer on the nonnegativity of M_{C1}(m,n) and M_{C5}(m,n)
by: He, Bing, et al.
Published: (2025)

The $m$-th Element of a Sidon Set
by: Balasubramanian, R., et al.
Published: (2024)

Frobenius numbers associated with Diophantine triples of $x^2+y^2=z^r$ (extended version)
by: Komatsu, Takao, et al.
Published: (2024)

Sárközy's Theorem in Various Finite Field Settings
by: Li, Anqi, et al.
Published: (2022)

The entries of the Sinkhorn limit of an $m \times n$ matrix
by: Rowland, Eric, et al.
Published: (2024)

A Proof of Bala's General-$m$ Representation of the Harmonic Numbers
by: Niu, Tong
Published: (2026)

Some zero-sum problems over $\langle x,y \mid x^2 = y^{n/2}, y^n = 1, yx = xy^s \rangle$
by: Ribas, Sávio
Published: (2025)

Denominator identity for the affine Lie superalgebra $\widehat{\mathfrak{spo}}(2m,2m+1)$ and indefinite theta functions
by: Matsusaka, Toshiki, et al.
Published: (2025)

Periodicity and Dynamical Systems of Dickson Polynomials in Finite Fields
by: Peng, Wayne, et al.
Published: (2025)

Bounds for monochromatic solutions to $\{x+y,xy\}$
by: Green, Ben, et al.
Published: (2025)

On the number of subgroups of the group $\mathbb{Z}_{m_{1}} \times \mathbb{Z}_{m_{2}}$ with $m_{1}m_{2}\leq x$ such that $m_{1}m_{2}$ is a $k$-th power
by: Sui, Yankun, et al.
Published: (2025)

The Probabilistic Zeta Function of a Finite Lattice
by: Shala, Besfort
Published: (2021)

Scattered Behavior Using Modified Cyclotomic Mapping Over Finite Fields Of Odd Characteristic
by: Mondal, Suman
Published: (2025)

On some conjectural supercongruences involving the sequence $t_n(x)$
by: Han, Hui-Li, et al.
Published: (2025)

On the stopping time of the Collatz map in $\mathbb{F}_2[x]$
by: Alon, Gil, et al.
Published: (2024)

An easy proof of Ramanujan's famous congruences $p(5m+4)\equiv 0 \equiv τ(5m+5) \pmod 5$
by: Bal, Hartosh Singh, et al.
Published: (2025)

The number of non-isomorphic arithmetic expressions that can be constructed using +,-,x and /
by: Cohen, Boaz
Published: (2026)

On a conjectural supercongruence involving the dual sequence $s_n(x)$
by: Wang, Chen, et al.
Published: (2025)

The Number of Solutions to $ax+by+cz=n$ for Fibonacci and Lucas triplets
by: Teotia, Pooja
Published: (2026)

$q$-Congruences for Z.-W. Sun's generalized polynomials $w^{(α)}_k(x)$
by: Li, Lin-Yue, et al.
Published: (2025)

Edge Zeta Functions and Eigenvalues for Buildings of Finite Groups of Lie Type
by: Shen, Jianhao
Published: (2024)

Freiman's $3k-4$ Theorem for Function Fields
by: Couvreur, Alain, et al.
Published: (2024)

On the Natural Density of Monic Integer Polynomials with Roots in a Fixed Number Field
by: Fatehizadeh, Amirali
Published: (2026)

Ramanujan Complexes from Unitary Groups over Number Fields
by: Dalal, Rahul, et al.
Published: (2026)

On the polynomial equation $P(Q(x_1,\ldots,x_m))=Q(P(x_1),\ldots,P(x_m))$
by: Mingajev, Arseny
Published: (2024)

The Fractal and The Recurrence Equations Concerning The Integer Partitions
by: Zhang, Meng
Published: (2013)

Arithmetic properties of $(\ell,m)$-regular colored partitions
by: N., Yashas, et al.
Published: (2025)

On the Sidon tails of $\left\{\lfloor x^n\rfloor\right\}$
by: Dutta, Sayan
Published: (2026)

Non-permutation phenomena in trivariate families over $\F_{2^m}$ and resolution of a conjecture
by: Bartoli, Daniele, et al.
Published: (2024)

Modular Nahm sums for symmetrizable matrices of indices $({2,\ldots, 2},1)$ and $({1,\ldots, 1},2)$
by: Du, Julia Q. D., et al.
Published: (2026)

The compositional inverses of permutation polynomials of the form $\sum_{i=1}^kb_i(x^{p^m}+x+δ)^{s_i}-x$ over $\mathbb{F}_{p^{2m}}$
by: Wu, Danyao, et al.
Published: (2024)

On the Diophantine Equations $J_n +J_m =L_k$ and $L_n +L_m =J_k$
by: Salah, Osama, et al.
Published: (2024)

Exact formula for 1-lower run overpartitions
by: Mauth, Lukas
Published: (2023)

The inequality on the number of $1$-hooks, $2$-hooks and $3$-hooks in $t$-regular partitions
by: Lin, Hongshu, et al.
Published: (2025)

Quantitative bounds in the inverse theorem for the Gowers $U^{s+1}$-norms over cyclic groups
by: Manners, Frederick
Published: (2018)

Quantum Algorithms for Gowers Norm Estimation, Polynomial Testing, and Arithmetic Progression Counting over Finite Abelian Groups
by: Kuo, En-Jui
Published: (2025)

Solutions to $\sum_{i=1}^n 1/x_i=1$ in integers $p^a\,q^b$ with $p$ and $q$ two set primes
by: Levaillant, Claire I.
Published: (2026)