Results 81 to 90 of about 1,205,224 (205)
Symmetric Diophantine Equations
Rocky Mountain Journal of Mathematics, 2004 The author describes a method to obtain infinite parametric solutions of some Diophantine equations of type \(f(x,y)=f(u,v)\) where \(f\) is a form (usually the product of some linear and quadratic forms) with rational coefficients. The main idea is to apply a non-singular linear transformation \(x=\alpha u+\beta v\), \(y=\gamma u+\delta v\) such that ...
openaire +2 more sources
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
wiley +1 more source
Open Computer Science, 2018 We define a computable function f from positive integers to positive integers. We formulate a hypothesis which states that if a system S of equations of the forms xi· xj = xk and xi + 1 = xi has only finitely many solutions in non-negative integers x1, .
Tyszka Apoloniusz
doaj +1 more source
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
wiley +1 more source
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
wiley +1 more source
An exploration of Diophantine equations [PDF]
, 2012 This paper outlines recent research on Diophantine equations. The topics discussed include methods for generating solutions to specific equations and analysis of patterns in solutions to some specific ...
Hoffmaster, Christina Diane
core +3 more sources
The matrix diophantine equations $AX + BY = C$
Karpatsʹkì Matematičnì Publìkacìï, 2013 A method of constructing of solutions of matrix Diophantine equations $AX + BY = C$ over commutative domains of finitely generated principal ideals is suggested. The formulas of general solutions of such equations in some cases is proposed. The criterion
N. S. Dzhaliuk, V. M. Petrychkovych
doaj +1 more source
Diophantine equations in separated variables and polynomial power sums. [PDF]
Mon Hefte Math, 2021 Fuchs C, Heintze S.
europepmc +1 more source
The diophantine equation r2+r(x+y)=kxy
International Journal of Mathematics and Mathematical Sciences, 1985 The Diophantine equation of the title is solved in integers.
W. R. Utz
doaj +1 more source
Multiplicative Diophantine equations
Journal of Number Theory, 1992 The solution of the diophantine equation \(\prod_{i=1}^ n x_ i= \prod_{i=1}^ n y_ i\) is given in terms of \(n^ 2\) parameters (Bell's theorem) [cf. the first author, Proc. Ramanujan Cent. Int. Conf., Annamalainagar/India 1987, RMS Publ. 1, 141-146 (1988; Zbl 0696.10014)].
Srinivasa Rao, K. +2 more
openaire +1 more source