Entire Solutions of the Second-Order Fermat-Type Differential-Difference Equation
Journal of Mathematics, 2020 In this paper, the entire solutions of finite order of the Fermat-type differential-difference equation f″z2+△ckfz2=1 and the system of equations f1″z2+△ckf2z2=1 and f2″z2+△ckf1z2=1 have been studied.
Guoqiang Dang, Jinhua Cai
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A Matrix Approach by Convolved Fermat Polynomials for Solving the Fractional Burgers’ Equation
MathematicsThis article employs certain polynomials that generalize standard Fermat polynomials, called convolved Fermat polynomials, to numerically solve the fractional Burgers’ equation.
Waleed Mohamed Abd-Elhameed +4 more
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On solutions of a certain nonlinear differential-difference functional equation [PDF]
Mathematica BohemicaWe investigate all the possible finite order entire solutions of the Fermat-type differential-difference functional equation $(Af(z))^2+R^2(z)(Bf^{(m)}(z+c)+Cf^{(n)}(z))^2=Q(z)$, where $m,n\in\mathbb{N}$, $A,B,C\in\mathbb{C}\setminus\{0\}$ and $R(z)$, $Q(
Rajib Mandal, Raju Biswas
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The geometry of trifocal curves with applications in architecture, urban and spatial planning [PDF]
Spatium, 2014 In this paper we consider historical genesis of trifocal curve as an optimal curve for solving the Fermat’s problem (minimizing the sum of distance of one point to three given points in the plane). Trifocal curves are basic plane geometric forms
Petrović Maja +2 more
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Further Results about a Special Fermat-Type Difference Equation
Journal of Function Spaces, 2020 In this paper, we prove the difference equation Fz3+ΔcFz+c3=1 does not have meromorphic solution of finite order over the complex plane C. We also discuss an application to the unique range set problem.
Hongwei Ma, Jianming Qi, Zhenjie Zhang
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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
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Lattice Points on the Fermat Factorization Method
Journal of Mathematics, 2022 In this paper, we study algebraic properties of lattice points of the arc on the conics x2−dy2=N especially for d=1, which is the Fermat factorization equation that is the main idea of many important factorization methods like the quadratic field sieve ...
Regis Freguin Babindamana +2 more
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Trigonometric Polynomial Solutions of Bernoulli Trigonometric Polynomial Differential Equations
Mathematics, 2022 We consider real trigonometric polynomial Bernoulli equations of the form A(θ)y′=B1(θ)+Bn(θ)yn where n≥2, with A,B1,Bn being trigonometric polynomials of degree at most μ≥1 in variables θ and Bn(θ)≢0.
Claudia Valls
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GENERALIZED LUCAS PRIMES IN THE FERMAT-EULER EQUATION [PDF]
Journal of Algebraic SystemsThe property of having infinitely many prime numbers award these numbers to have many applications in various fields of sciences. One of the most important applications is their use in the creation of many public key cryptosystems' private keys ...
Hayder Hashim
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Entire solutions for several complex partial differential-difference equations of Fermat type in ℂ2
Open Mathematics, 2021 By utilizing the Nevanlinna theory of meromorphic functions in several complex variables, we mainly investigate the existence and the forms of entire solutions for the partial differential-difference equation of Fermat type α∂f(z1,z2)∂z1+β∂f(z1,z2)∂z2m+f(
Gui Xian Min +3 more
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