Results 71 to 80 of about 918 (182)
The Solution of a Diophantine Equation [PDF]
Proceedings of the American Mathematical Society, 1952 in which we suppose that f(y) =f(yi, * ya) is a homogeneous polynomial, with integral coefficients, of degree m, where m is of the form 2P(2q+1), q being a non-negative integer, p is one of the integers 0, 1, * * *, n -1, and thus m 0 0 (mod 2n). We suppose further that the rank of the matrix of the forms Enl aajx (i= 1, , 2n) is 2n -1 and thus we may ...
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Matrix Diophantine equations over quadratic rings and their solutions
Karpatsʹkì Matematičnì Publìkacìï, 2020 The method for solving the matrix Diophantine equations over quadratic rings is developed. On the basic of the standard form of matrices over quadratic rings with respect to $(z,k)$-equivalence previously established by the authors, the matrix ...
N.B. Ladzoryshyn +2 more
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On the exceptional set in Littlewood's discrete conjecture
Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.Abstract We consider a discrete analogue of the well‐known Littlewood conjecture on Diophantine approximations and obtain a strong upper bound for the number of exceptional vectors in this conjecture.
I. D. Shkredov
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IEEE AccessThe Objectives of this study is to extend the concept of q-rung linear Diophantine fuzzy sets (q-RLDFSs), followed by the Near-Earth Asteroids (NEAs) deflection detector.
Maria Shams +4 more
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Double‐jump phase transition for the reverse Littlewood–Offord problem
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract Erdős conjectured in 1945 that for any unit vectors v1,…,vn$v_1, \ldots, v_n$ in R2$\mathbb {R}^2$ and signs ε1,…,εn$\varepsilon _1, \ldots, \varepsilon _n$ taken independently and uniformly in {−1,1}$\lbrace -1,1\rbrace$, the random Rademacher sum σ=ε1v1+⋯+εnvn$\sigma = \varepsilon _1 v_1 + \cdots + \varepsilon _n v_n$ satisfies ∥σ∥2⩽1$\Vert \
Lawrence Hollom +2 more
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Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract We survey ideas surrounding the study of the number of integers that can be represented as the sum of three positive cubes. We focus on the early contribution of Davenport using elementary techniques, and the subsequent developments due to Vaughan, which introduced Fourier analysis and mirrored many of the important developments of the Hardy ...
James Maynard
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Adjugates of Diophantine Quadruples [PDF]
Integers, 2010 AbstractDiophantine
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HNN extensions and embedding theorems for groups
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract The Higman–Neumann–Neumann (HNN) paper of 1949 is a landmark of group theory in the 20th century. The proof of its main theorem covers less than a page and uses only pre‐existing technology, but the construction that it introduced, the HNN extension, quickly became one of the principal tools of combinatorial group theory, widely used to build ...
Martin R. Bridson +1 more
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A Linear Diophantine Fuzzy Graph-Theoretic Approach for Planar Dynamic Traffic Optimization
Applied Computational Intelligence and Soft ComputingDynamic urban traffic signal control systems face uncertainties such as fluctuating vehicle densities, unpredictable incidents, and varying driver behaviors, making precise decision-making highly challenging.
Waheed Ahmad Khan +4 more
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On the Relationship Between Matiyasevich's and Smorynski's Theorems
Scientific Annals of Computer Science, 2019 Let R be a non-zero subring of Q with or without 1. We assume that for every positive integer n there exists a computable surjection from N onto Rn. Every R \in {Z,Q} satisfi es these conditions.
Agnieszka Peszek, Apoloniusz Tyszka
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