Results 21 to 30 of about 7,755,587 (178)
Journal of Mathematics, 2021 This article is mainly concerned with the existence and the forms of entire solutions for several systems of the second-order partial differential difference equations of Fermat type α∂2f1z1,z2/∂z12+β∂2f1z1,z2/∂z22n1+f2z1+c1,z2+c2m1=1α∂2f2z1,z2/∂z12+β ...
Si Min Liu, Hong Yan Xu
doaj +1 more source
The Exact Solutions for Several Partial Differential-Difference Equations with Constant Coefficients
Mathematics, 2022 This article is concerned with the description of the entire solutions of several Fermat type partial differential-difference equations (PDDEs) μf(z)+λfz1(z)2+[αf(z+c)−βf(z)]2=1, and μf(z)+λ1fz1(z)+λ2fz2(z)2+[αf(z+c)−βf(z)]2=1, where fz1(z)=∂f∂z1 and fz2(
Hongyan Xu +2 more
doaj +1 more source
How Galileo dropped the ball and Fermat picked it up [PDF]
, 2009 This paper introduces a little-known episode in the history of physics, in which a mathematical proof by Pierre Fermat vindicated Galileo's characterization of freefall.
Roberts, Bryan W.
core +1 more source
Open Mathematics, 2023 Our purpose in this article is to describe the solutions of several product-type nonlinear partial differential equations (PDEs) (a1u+b1uz1+c1uz2)(a2u+b2uz1+c2uz2)=1,\left({a}_{1}u+{b}_{1}{u}_{{z}_{1}}+{c}_{1}{u}_{{z}_{2}})\left({a}_{2}u+{b}_{2}{u}_{{z}_{
Xu Yi Hui +3 more
doaj +1 more source
Mixed-type functional differential equations: A numerical approach [PDF]
, 2007 This is a PDF version of a preprint submitted to Elsevier. The definitive version was published in Journal of Computational and Applied Mathematics and is available at www.elsevier.comThis preprint discusses mixed-type functional ...
Ford, Neville J., Lumb, Patricia M.
core +1 more source
Random Thue and Fermat equations [PDF]
, 2015 We consider Thue equations of the form axk+byk=1, and assuming the truth of the abc-conjecture, we show that almost all locally soluble Thue equations of degree at least three violate the Hasse principle.
Marmon, Oscar, Dietmann, Rainer
core +1 more source
The Fermat-type equation with signature (2, 2, n) and Bunyakovsky conjecture
Songklanakarin Journal of Science and Technology (SJST), 2022 We first discuss the Fermat-type equation with signature (2, 𝑚, 𝑛), which is the Diophantine equation in the shape 𝑥 2 + 𝑦 𝑚 = 𝑧 𝑛 , where 𝑥, 𝑦 and 𝑧 are unknown integers, and 𝑚, 𝑛 are fixed positive integers greater than 1.
Sawian Jaidee, Korakot Saosoong
doaj +1 more source
On Entire solutions of system of Fermat-type difference and partial differential-difference equations in $\mathbb{C}^n$ [PDF]
, 2023 The equation $f^n+g^n=1$, $n\in\mathbb{N}$ can be regarded as the Fermat Diophantine equation over the function field. In this paper we study the characterization of entire solutions of some system of Fermat type functional equations by taking $e^{g_1(z)}
Haldar, Goutam
core +1 more source
On a Fermat-Type Diophantine Equation
Journal of Number Theory, 2000 The equation mentioned in the title is (*) \(x^p+y^p=pcz^p\), where \(p\) is a prime \(>3\) and \(c\) is an integer whose prime factors are of the form \(kp-1\), \((k,p)=1\). Equations of this type, with the coefficient \(pc\) replaced by integers satisfying various conditions, have been the subject of several studies, mainly in the case that \(x,y,z\)
openaire +2 more sources
An application of the symplectic argument to some Fermat-type equations
Comptes Rendus. Mathématique, 2016 Let p be a prime number. In the early 2000s, it was proved that the Fermat equations with coefficients 3 x
Freitas, Nuno, Kraus, Alain
openaire +2 more sources