Results 81 to 90 of about 92,931 (194)

Exponential Diophantine equations [PDF]

Pacific Journal of Mathematics, 1982
Brenner, J. L., Foster, Lorraine L.
openaire   +3 more sources

On a conjecture concerning the exponential Diophantine equation $ (an^{2}+1)^{x}+(bn^{2}-1)^{y} = (cn)^{z} $

Electronic Research Archive
Let $ a $, $ b $, $ c $, and $ n $ be positive integers such that $ a+b = c^{2} $, $ 2\nmid c $ and $ n > 1 $. In this paper, we prove that if $ \gcd(c, n) = 1 $ and $ n\geq 117.14c $, then the equation $ (an^{2}+1)^{x}+(bn^{2}-1)^{y} = (cn)^{z} $ has ...
Shuanglin Fei, Guangyan Zhu, Rongjun Wu
semanticscholar   +1 more source

Exponential diophantine equations with four terms

Indagationes Mathematicae, 1992
This article gives some examples how to make exponential diophantine equations more practical. The authors take the large exponential bounds for solutions given by Baker's method to computational available bounds. Let \(p\) and \(q\) be distinct primes less than 200. The main theorems are: (1) Every solution of the equation \(p^ x q^ y\pm p^ z \pm q^ w
Deze, Mo, Tijdeman, R.
openaire   +2 more sources

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 ...
openaire   +2 more sources

Mixing Rates of the Geometrical Neutral Lorenz Model. [PDF]

J Stat Phys, 2023
Bruin H, Canales Farías HH.
europepmc   +1 more source

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

On prime powers in linear recurrence sequences. [PDF]

Ann Math Quebec, 2023
Odjoumani J, 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.
openaire   +2 more sources

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