Solving Diophantine Equations on a Network of Workstations

On Solving Linear Diophantine Systems Using Generalized Rosser's Algorithm

Utilizing a new feed-back fuzzy neural network for solving a system of fuzzy equations

This paper intends to offer a new iterative method based on articial neural networks for finding solution of a fuzzy equations system. Our proposed fuzzied neural network is a ve-layer feedback neural network that corresponding connection weights to output layer are fuzzy numbers. This architecture of articial neural networks, can get a real input vector and calculates its corresponding fuzzy o...

Explicit Methods for Solving Diophantine Equations

We give a survey of some classical and modern methods for solving Diophantine equations.

Solving nonlinear Lane-Emden type equations with unsupervised combined artificial neural networks

In this paper we propose a method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-innite domain. The proposed approach is based on an Unsupervised Combined Articial Neural Networks (UCANN) method. Firstly, The trial solutions of the differential equations are written in the form of feed-forward neural networks cont...

A Generalized Fibonacci Sequence and the Diophantine Equations $x^2pm kxy-y^2pm x=0$

In this paper some properties of a generalization of Fibonacci sequence are investigated. Then we solve the Diophantine equations $x^2pmkxy-y^2pm x=0$, where $k$ is positive integer, and describe the structure of solutions.