$S$-unit equations and the asymptotic Fermat conjecture over number fields [PDF]
, 2022 Recent attempts at studying the Fermat equation over number fields haveuncovered an unexpected and powerful connection with $S$-unit equations. Inthis expository paper we explain this connection and its implications for theasymptotic Fermat conjecture.
Ozman, E. ; https://orcid.org/ +1 more
core
Solutions of several general quadratic partial differential-difference equations in ℂ2
Demonstratio MathematicaIn this article, we have introduced general transformation to solving the general quadratic equations. It is of interest to know about the existence and form of the solutions of general quadratic functional equations.
Ahamed Molla Basir, Mandal Sanju
doaj +1 more source
An Efficient Grid-Based Geocasting Scheme for Wireless Sensor Networks. [PDF]
Sensors (Basel), 2023 Wang NC +4 more
europepmc +1 more source
Derivation of closed-form ellipsoidal X-ray mirror shapes from Fermat's principle. [PDF]
J Synchrotron Radiat, 2022 Goldberg KA.
europepmc +1 more source
Micromixer with Fine-Tuned Mathematical Spiral Structures. [PDF]
ACS Omega, 2021 Yin B +5 more
europepmc +1 more source
A Variational Framework for Fermat-Type Equations
This paper establishes a continuous variational framework to resolve Fermat-type equations ($x^n + y^n = z^n$). By evaluating the continuous geometric volume against the absolute rigidity of the discrete integer lattice, we expose a fundamental structural incompatibility.
openaire +1 more source
Fermat's treatise on quadrature: A new reading [PDF]
The Treatise on Quadrature of Fermat (c. 1659), besides containing the first known proof of the computation of the area under a higher parabola, R x+m/n dx, or under a higher hyperbola, R x-m/n dx— with the appropriate limits of integration in each case—,
Josep Pla +2 more
core
Level Lowering Modulo Prime Powers and Twisted Fermat Equations
, 2012 We discuss a clean level lowering theorem modulo prime powers for weight 2 cusp forms. Furthermore, we illustrate how this can be used to completely solve certain twisted Fermat equations axn + byn + czn = 0.
Dahmen, Sander R.; id_orcid +3 more
core +1 more source
Asymptotic Fermat\u27s Last Theorem for a family of equations of signature $(2, 2n, n)$ [PDF]
In this paper, we study the integer solutions of a family of Fermat-type equations of signature $(2, 2n, n)$, $Cx^2 + q^ky^{2n} = z^n$. We provide an algorithmically testable set of conditions which, if satisfied, imply the existence of a constant $B_{C,
García, Pedro-José Cazorla
core +1 more source
Genetic algorithm optimization of heliostat field layout for the design of a central receiver solar thermal power plant. [PDF]
Heliyon, 2023 Haris M +8 more
europepmc +1 more source