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Random Diophantine equations in the primes II

Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.
Abstract Let d⩾2$d\geqslant 2$ and n⩾d$n\geqslant d$ with (d,n)∉{(2,2),(3,3)}$(d,n)\notin \lbrace (2,2),(3,3)\rbrace$. We consider homogeneous Diophantine equations of degree d$d$ in n+1$n+1$ variables and whether they have solutions in the primes.
Philippa Holdridge
wiley   +1 more source

Tessellation Groups, Harmonic Analysis on Non‐Compact Symmetric Spaces and the Heat Kernel in View of Cartan Convolutional Neural networks

Fortschritte der Physik, Volume 74, Issue 4, April 2026.
ABSTRACT In this paper, we continue the development of the Cartan neural networks programme, launched with three previous publications, by focusing on some mathematical foundational aspects that we deem necessary for our next steps forward. The mathematical and conceptual results are diverse and span various mathematical fields, but the inspiring ...
Pietro Fré, Federico Milanesio, Marcelo Oyarzo, Matteo Santoro, Mario Trigiante   +4 more
wiley   +1 more source

The Diophantine equation ax2+2bxy−4ay2=±1

International Journal of Mathematics and Mathematical Sciences, 2003
We discuss, with the aid of arithmetical properties of the ring of the Gaussian integers, the solvability of the Diophantine equation ax2+2bxy−4ay2=±1, where a and b are nonnegative integers.
Lionel Bapoungué
doaj   +1 more source

On the Diophantine equation 2x + 11y = z2 [PDF]

Maejo International Journal of Science and Technology, 2013
In this paper it is shown that (3,0,3) is the only non-negative integer solution of the Diophantine equation 2x + 11y = z2.
Somchit Chotchaisthit
doaj  

Diophantine Solutions Based Permutation for Image Encryption

Journal of Algorithms & Computational Technology, 2013
A permutation technique based on the resolution of the system of three independent Diophantine equations is presented. Each Diophantine equation parameters are two positive integers generated from a chaotic system.
J. S. Armand Eyebe Fouda, J. Yves Effa, Bertrand Bodo, Maaruf Ali   +3 more
doaj   +1 more source

On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences. [PDF]

Ramanujan J, 2021
Ddamulira M, Luca F.
europepmc   +1 more source

On a Diophantine Equation of Stroeker

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2010
The authors prove that there are infinitely many positive integers \(N\) such that the Diophantine equation \((x^2+y)(x+y^2)=N(x-y)^3\) has no nontrivial integer solution \((x,y)\).
Luca, Florian, Stănică, Pantelimon, Togbé, Alain   +2 more
openaire   +4 more sources

Symmetric Diophantine Equations

Rocky Mountain Journal of Mathematics, 2004
The author describes a method to obtain infinite parametric solutions of some Diophantine equations of type \(f(x,y)=f(u,v)\) where \(f\) is a form (usually the product of some linear and quadratic forms) with rational coefficients. The main idea is to apply a non-singular linear transformation \(x=\alpha u+\beta v\), \(y=\gamma u+\delta v\) such that ...
openaire   +2 more sources

Separable Diophantine equations [PDF]

Transactions of the American Mathematical Society, 1945
Theoretically, as noted by Skolem [3, p. 21(1), the general problem of algebraic diophantine analysis is reducible to the case in which occur only equations and inequalities of degree not higher than the second. For the extensive class of separable systems defined in ?6, this reduction can be performed effectively, eventuating in the complete integer ...
openaire   +2 more sources

On the Diophantine Equation x2 – kxy + ky2 + ly = 0, l = 2n

Annals of the West University of Timisoara: Mathematics and Computer Science, 2017
We consider the Diophantine equation x2-kxy+ky2+ ly = 0 for l = 2n and determine for which values of the odd integer k, it has a positive integer solution x and y.
Mavecha Sukrawan
doaj   +1 more source