Results 71 to 80 of about 1,205,224 (205)

On a diophantine equation

, 1967
Formulae are given furnishing all non-trivial integer solutions of the equation \[ (x^2-t^2)(y^2-t^2)=\biggl(\biggl({y-x\over 2}\biggr)^2-t^2\biggr)^2 \] considered for \(t=1\) by the reviewer and \textit{W. Sierpiński} [Elem. Math. 18, 132--133 (1963; Zbl 0126.07301)].
openaire   +2 more sources

A Repulsion Motif in Diophantine Equations [PDF]

The American Mathematical Monthly, 2011
Problems related to the existence of integral and rational points on cubic curves date back at least to Diophantus. A significant step in the modern theory of these equations was made by Siegel, who proved that a non-singular plane cubic equation has only finitely many integral solutions.
Everest, G, Ward, T
openaire   +6 more sources

New results on embeddings of self‐similar sets via renormalization

Proceedings of the London Mathematical Society, Volume 133, Issue 1, July 2026.
Abstract For self‐similar sets X,Y⊆R$X,Y\subseteq \mathbb {R}$, we obtain new results toward the affine embeddings conjecture of Feng–Huang–Rao (2014), and the equivalent weak intersections conjecture. We show that the conjecture holds when the defining maps of X,Y$X,Y$ have algebraic contraction ratios, and also for arbitrary Y$Y$ when the maps ...
Amir Algom, Michael Hochman, Meng Wu
wiley   +1 more source

Separable Diophantine equations [PDF]

Transactions of the American Mathematical Society, 1945
Theoretically, as noted by Skolem [3, p. 21(1), the general problem of algebraic diophantine analysis is reducible to the case in which occur only equations and inequalities of degree not higher than the second. For the extensive class of separable systems defined in ?6, this reduction can be performed effectively, eventuating in the complete integer ...
openaire   +2 more sources

Kripke on Gödel Incompleteness

Theoria, Volume 92, Issue 3, June 2026.
ABSTRACT This paper surveys six of Saul Kripke's highly creative ideas and results on Gödel incompleteness, from when he was an undergraduate to last publications. These include his extension of incompleteness from sentences to predicates, his model‐theoretic proof of incompleteness of arithmetic, his compelling analysis of incompleteness in terms of ...
Daniel Isaacson
wiley   +1 more source

Generalized free wreath products and their operator algebras

Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.
Abstract We develop a new approach on free wreath products, generalizing the constructions of Bichon and of Fima‐Pittau. We show stability properties for certain approximation properties such as exactness, Haagerup property, hyperlinearity, and K‐amenability. We study qualitative properties of the associated von Neumann algebra: factoriality, primeness,
Pierre Fima, Arthur Troupel
wiley   +1 more source

Moderate Deviation Principles for Lacunary Trigonometric Sums

Mathematische Nachrichten, Volume 299, Issue 5, Page 1028-1044, May 2026.
ABSTRACT Classical works of Kac, Salem, and Zygmund, and Erdős and Gál have shown that lacunary trigonometric sums despite their dependency structure behave in various ways like sums of independent and identically distributed random variables. For instance, they satisfy a central limit theorem (CLT) and a law of the iterated logarithm.
Joscha Prochno, Marta Strzelecka
wiley   +1 more source

On a few Diophantine equations, in particular, Fermat's last theorem

International Journal of Mathematics and Mathematical Sciences, 2003
This is a survey on Diophantine equations, with the purpose being to give the flavour of some known results on the subject and to describe a few open problems.
C. Levesque
doaj   +1 more source

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
wiley   +1 more source

On some diophantine equations involving factorials [PDF]

Mathematica Bohemica
We study the Diophantine equations $(n!)^k - n^k = (k!)^n - k^n$ and $(n!)^k + n^k = (k!)^n + k^n$, where $k$ and $n$ are positive integers. According to H. Arzel, F. Luca (2017), only the first equation has nontrivial solutions. It is proved also that ${
Maciej Gnatowski
doaj   +1 more source