Results 31 to 40 of about 287 (124)

Euclidean algorithms are Gaussian over imaginary quadratic fields

Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.
Abstract We prove that the distribution of the number of steps of the Euclidean algorithm of rationals in imaginary quadratic fields with denominators bounded by N$N$ is asymptotically Gaussian as N$N$ goes to infinity, extending a result by Baladi and Vallée for the real case.
Dohyeong Kim, Jungwon Lee, Seonhee Lim
wiley   +1 more source

Iitaka fibrations and integral points: A family of arbitrarily polarized spherical threefolds

Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.
Abstract Studying Manin's program for a family of spherical log Fano threefolds, we determine the asymptotic number of integral points whose height associated with an arbitrary ample line bundle is bounded. This confirms a recent conjecture by Santens and sheds new light on the logarithmic analog of Iitaka fibrations, which have not yet been adequately 
Ulrich Derenthal, Florian Wilsch
wiley   +1 more source

A Learner‐Centred Exploration of Teachers' Solution Pathways in K‐12 Programming‐Based Mathematical Problem‐Solving

Journal of Computer Assisted Learning, Volume 41, Issue 5, October 2025.
ABSTRACT Background Empirical studies have revealed students' development of computational thinking (CT) and mathematical thinking (MT) during programming‐based mathematical problem‐solving, highlighting specific CT concepts or practices that serve as learning goals or outcomes.
Huiyan Ye, Biyao Liang, Oi‐Lam Ng
wiley   +1 more source

Inhomogeneous Khintchine–Groshev theorem without monotonicity

Bulletin of the London Mathematical Society, Volume 57, Issue 9, Page 2639-2657, September 2025.
Abstract The Khintchine–Groshev theorem in Diophantine approximation theory says that there is a dichotomy of the Lebesgue measure of sets of ψ$\psi$‐approximable numbers, given a monotonic function ψ$\psi$. Allen and Ramírez removed the monotonicity condition from the inhomogeneous Khintchine–Groshev theorem for cases with nm⩾3$nm\geqslant 3$ and ...
Seongmin Kim
wiley   +1 more source

A circle method approach to K‐multimagic squares

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract In this paper, we investigate K$K$‐multimagic squares of order N$N$. These are N×N$N \times N$ magic squares that remain magic after raising each element to the k$k$th power for all 2⩽k⩽K$2 \leqslant k \leqslant K$. Given K⩾2$K \geqslant 2$, we consider the problem of establishing the smallest integer N2(K)$N_2(K)$ for which there exist ...
Daniel Flores
wiley   +1 more source

On Bureau's Classification of Quadratic Differential Equations in Two Variables Free of Movable Critical Points

Studies in Applied Mathematics, Volume 155, Issue 2, August 2025.
ABSTRACT As part of the efforts aimed at extending Painlevé and Gambier's work on second‐order equations in one variable to first‐order ones in two, in 1981, Bureau classified the systems of ordinary quadratic differential equations in two variables which are free of movable critical points (which have the Painlevé Property).
Adolfo Guillot
wiley   +1 more source

ArtEM: Enhancing the Understanding of Integer and Modular Arithmetic Through Interactive Learning Software

Computer Applications in Engineering Education, Volume 33, Issue 4, July 2025.
ABSTRACT Integer and modular arithmetic is a fundamental area of mathematics, with extensive applications in computer science, and is essential for cryptographic protocols, error correction, and algorithm efficiency. However, students often struggle to understand its abstract nature, especially when transitioning from theoretical knowledge to practical
Violeta Migallón, Héctor Penadés, Jose Penadés   +2 more
wiley   +1 more source

Homogeneous Quadratic Equation with Four Unknowns 𝑥2 + 𝑥𝑦 + 𝑦2 = 𝑧2 + 𝑧𝑤 + 𝑤2

Indian Journal of Science and Technology
Objectives: Diophantine research focuses on various ways to tackle multi variable and multi-degree Diophantine problems. A Diophantine equation is a polynomial equation with only integer solutions.
R. Sathiyapriya, M. Gopalan
semanticscholar   +1 more source

Localized and Extended Phases in Square Moiré Patterns

Annalen der Physik, Volume 537, Issue 6, June 2025.
Rotated superimposed lattices in two dimensions, the termed moiré patterns, represent a clear example of how the structure affects the physical properties of a particle moving on it. A robust numerical treatment of continuous and discrete models leads to confirm that while localized states result from angles that produce non‐commensurable lattices ...
C. Madroñero, G. A. Domínguez‐Castro, R. Paredes   +2 more
wiley   +1 more source

On the x-coordinates of Pell equations that are sums of two Padovan numbers. [PDF]

Bol Soc Mat Mex, 2021
Ddamulira M.
europepmc   +1 more source