Results 31 to 40 of about 1,510,077 (175)
On the Diophantine Equation $(8r^2+1)^x+(r^2-1)^y=(3r)^z$ Regarding Terai's Conjecture
Communications in Advanced Mathematical SciencesThis study establishes that the sole positive integer solution to the exponential Diophantine equation $(8r^2+1)^x+(r^2-1)^y=(3r)^z$ is $(x,y,z)=(1,1,2)$ for all $r>1$.
Murat Alan, Tuba Çokoksen
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Nonlinear-Adaptive Mathematical System Identification
Computation, 2017 By reversing paradigms that normally utilize mathematical models as the basis for nonlinear adaptive controllers, this article describes using the controller to serve as a novel computational approach for mathematical system identification.
Timothy Sands
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On 7‐adic Galois representations for elliptic curves over Q$\mathbb {Q}$
Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.Abstract In recent years, significant progress has been made on Mazur's Program B, with many authors beginning a systematic classification of all possible images of p$p$‐adic Galois representations attached to elliptic curves over Q$\mathbb {Q}$. Currently, the classification is only complete for p∈{2,3,13,17}$p \in \lbrace 2,3,13,17\rbrace$.
Lorenzo Furio, Davide Lombardo
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Zhejiang Daxue xuebao. Lixue ban, 2007 用渐近连分数的性质和Pell方程的解类特点，得到了指数丢番图方程的解（x，y，n）的性质及其较为精确的上界 ...
YANGShi-chun(杨仕椿), HEBo(何波)
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On the moments of exponential sums over r$r$‐free polynomials
Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.Abstract Let Fq[t]${\mathbb {F}}_q[t]$ denote the ring of polynomials over the finite field Fq${\mathbb {F}}_q$. Building off of techniques of Balog and Ruzsa and of Keil in the integer setting, we determine the precise order of magnitude of k$k$th moments of exponential sums over r$r$‐free polynomials in Fq[t]${\mathbb {F}}_q[t]$ for all k>0$k>0$.
Ben Doyle
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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 +2 more
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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
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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
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On the Diophantine equation $(2^x-1)(p^y-1)=2z^2$ [PDF]
, 2021 summary:Let $p$ be an odd prime. By using the elementary methods we prove that: (1) if $2\nmid x$, $p\equiv \pm 3\pmod 8,$ the Diophantine equation $(2^{x}-1)(p^{y}-1)=2z^{2}$ has no positive integer solution except when $p=3$ or $p$ is of the form $p ...
Tong, Ruizhou
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On the exponential diophantine equations of degree three [PDF]
, 2019 Diophantine equation is known as a polynomial equation with two or more unknowns which only integral solutions are sought. This paper concentrates on finding an integral solution to the exponential Diophantine equation of degree three.
Sapar, Siti Hasana +1 more
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