Results 51 to 60 of about 169 (152)

Exponential Diophantine equations [PDF]

Pacific Journal of Mathematics, 1982
Brenner, J. L., Foster, Lorraine L.
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Max–min of polynomials and exponential diophantine equations

Journal of Number Theory, 2010
In the first half of this paper, largely based on earlier work of \textit{R. Dvornicich, U. Zannier}, and the author [Acta Arith. 106, No. 2, 115--121 (2003; Zbl 1020.11018)], it is shown that for \(F \in {\mathbb Z}[x,y]\) one has \(\max_{x \in \mathbb Z \cap [-T,T]} \min_{y \in \mathbb Z} |F(x,y)| = o(T^{1/2})\) as \(T \to \infty\) if and only if ...
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On a variant of Pillai's problem involving <i>S</i>-units and Fibonacci numbers. [PDF]

Bol Soc Mat Mex, 2022
Ziegler V.
europepmc   +1 more source

An application of Frey's idea to exponential Diophantine equations

Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1994
Let \(a\), \(b\), \(c\), \(l\), \(m\), \(n\) be relatively prime positive integers. In this paper it is shown that the equation \(la^ x+ mb^ y= nc^ z\), has a finite number of solutions in positive integers \(x\), \(y\), \(z\), all of which can be effectively determined. The effective procedure is based on: a) \textit{G.
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Mixing Rates of the Geometrical Neutral Lorenz Model. [PDF]

J Stat Phys, 2023
Bruin H, Canales Farías HH.
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On prime powers in linear recurrence sequences. [PDF]

Ann Math Quebec, 2023
Odjoumani J, Ziegler V.
europepmc   +1 more source

Counting Real Roots in Polynomial-Time via Diophantine Approximation. [PDF]

Found Comut Math, 2022
Rojas JM.
europepmc   +1 more source

Integers representable as differences of linear recurrence sequences. [PDF]

Res Number Theory, 2021
Tichy R, Vukusic I, Yang D, Ziegler V.
europepmc   +1 more source

S-Unit Equations in Modules and Linear-Exponential Diophantine Equations

Proceedings of the 58th Annual ACM Symposium on Theory of Computing
Let $T$ be a positive integer, and $\mathcal{M}$ be a finitely presented module over the Laurent polynomial ring $\mathbb{Z}_{/T}[X_1^{\pm}, \ldots, X_N^{\pm}]$. We consider S-unit equations over $\mathcal{M}$: these are equations of the form $x_1 m_1 + \cdots + x_K m_K = m_0$, where the variables $x_1, \ldots, x_K$ range over the set of monomials ...
Ruiwen Dong, Doron Shafrir
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Parameter Identification of Model for Piezoelectric Actuators. [PDF]

Micromachines (Basel), 2023
Liu D, Dong J, Guo S, Tan L, Yu S.
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