Results 51 to 60 of about 4,013,096 (184)

Common values of two k-generalized Pell sequences [PDF]

Notes on Number Theory and Discrete Mathematics
Let k≥2 and let (Pₙ⁽ᵏ⁾)ₙ≥₂₋ₖ be the k-generalized Pell sequence defined by Pₙ⁽ᵏ⁾=2Pₙ₋₁⁽ᵏ⁾+2Pₙ₋₂⁽ᵏ⁾+...+2Pₙ₋ₖ⁽ᵏ⁾ for n≥2 with initial conditions P₋₍ₖ₋₂₎⁽ᵏ⁾=P₋₍ₖ₋₃₎⁽ᵏ⁾=...=P₋₁⁽ᵏ⁾=P₀⁽ᵏ⁾=0, and P₁⁽ᵏ⁾=1.
Zafer Şiar, Florian Luca, Faith Shadow Zottor   +2 more
doaj   +1 more source

Multiplicatively dependent integer vectors on a hyperplane

Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.
Abstract We establish several asymptotic formulae and upper bounds for the count of multiplicatively dependent integer vectors that lie on a fixed affine hyperplane and have bounded height. This work constitutes a direct extension of the results obtained by Pappalardi, Sha, Shparlinski, and Stewart.
Muhammad Afifurrahman, Valentio Iverson, Gian Cordana Sanjaya   +2 more
wiley   +1 more source

Definability of complex functions in o‐minimal structures

Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.
Abstract We prove that holomorphic continuations of functions in the classes an∗$\mathbf {an}^*$ and G$\mathcal {G}$ are definable in the o‐minimal structures Ran∗$\mathbb {R}_{\operatorname{an}^*}$ and RG$\mathbb {R}_{\mathcal {G}}$, respectively. More specifically, we give complex domains on which the holomorphic continuations are definable and show ...
Adele Padgett, Patrick Speissegger
wiley   +1 more source

On the Diophantine Equation $\left(9d^2 + 1\right)^x + \left(16d^2 - 1\right)^y = (5d)^z$ Regarding Terai's Conjecture

Journal of New Theory
This study proves that the Diophantine equation $\left(9d^2+1\right)^x+\left(16d^2-1\right)^y=(5d)^z$ has a unique positive integer solution $(x,y,z)=(1,1,2)$, for all $d>1$.
Murat Alan, Tuba Çokoksen
doaj   +1 more source

Solution of an odds inversion problem [PDF]

Notes on Number Theory and Discrete Mathematics
Consider the problem of determining the possible numbers of balls of two different colors in an urn such that if two are drawn out at random, the odds that they are different colors are a given value. We present a general solution of this problem for all
Robert K. Moniot
doaj   +1 more source

Random Diophantine equations in the primes

Mathematika, Volume 72, Issue 3, July 2026.
Abstract We consider equations of the form a1x1k+⋯+asxsk=0$a_{1}x_{1}^{k}+\cdots +a_{s}x_{s}^{k}=0$ where the variables xi$x_{i}$ are all taken to be primes. We define an analogue of the Hasse principle for solubility in the primes (which we call the prime Hasse principle), and prove that, whenever k⩾2$k\geqslant 2$, s⩾3k+2$s\geqslant 3k+2$, this holds
Philippa Holdridge
wiley   +1 more source

Multivariate discrete splines and linear Diophantine equations [PDF]

Transactions of the American Mathematical Society, 1993
In this paper we investigate the algebraic properties of multivariate discrete splines. It turns out that multivariate discrete splines are closely related to linear diophantine equations. In particular, we use a solvability condition for a system of linear diophantine equations to obtain a necessary and sufficient condition for the integer translates ...
openaire   +1 more source

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

On Terms of Generalized Fibonacci Sequences which are Powers of their Indexes

Mathematics, 2019
The k-generalized Fibonacci sequence ( F n ( k ) ) n (sometimes also called k-bonacci or k-step Fibonacci sequence), with k ≥ 2 , is defined by the values 0 , 0 , … , 0 , 1 of starting k its terms and such way ...
Pavel Trojovský
doaj   +1 more source

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