In this paper, we present an algorithm for solving directly linear Dio-phantine systems of both equations and inequations. Here directly means without adding slack variables for encoding inequalities as equalities. This algorithm is an extension of the algorithm due to Contejean and Devie 10] for solving linear Diophantine systems of equations, which is itself a generalization of the algorithm ...

Discrete truncate power is very useful for studying the number of nonnegative integer solutions of linear Diophantine equations. In this paper, some detail information about discrete truncated power is presented. To study the number of integer solutions of linear Diophantine inequations, the generalized truncated power and generalized discrete truncated power are defined and discussed respectiv...

Geometry and Diophantine equations have been ever-present in mathematics. Diophantus of Alexandria was born in the 3rd century (as far as we know), but a systematic mathematical study of word equations began only in the 20th century. So, the title of the present article does not seem to be justified at all. However, a linear Diophantine equation can be viewed as a special case of a system of wo...

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.

A lot of Scientific and Engineering problems require the solution of large systems of linear equations of the form b Ax in an effective manner. LU-Decomposition offers good choices for solving this problem. Our approach is to find the lower bound of processing elements needed for this purpose. Here is used the so called “Omega calculus”, as a computational method for solving problems via their ...

We globally classify two-component evolution equations, with homogeneous diagonal linear part, admitting infinitely many approximate symmetries. Important ingredients are the symbolic calculus of Gel’fand and Dikĭı, the Skolem–Mahler–Lech theorem, results on diophantine equations in roots of unity by F. Beukers, and an algorithm of C.J. Smyth.

Varying methods exist for computing a presentation of a finitely generated commutative cancellative monoid.We use an algorithm of Contejean andDevie [An efficient incremental algorithm for solving systems of linear diophantine equations, Inform. andComput. 113 (1994) 143–172] to show how these presentations can be obtained from the nonnegative integer solutions to a linear system of equations. ...

We use multivariate splines to investigate linear diophantine equations and related problems in graph theory. In particular, we solve a conjecture of Stanley about symmetric magic squares. 0 Elsevier Science Inc., 1997

The topic of this summer school was Diophantine equations, which are among the oldest studied mathematical objects. A Diophantine equation is an equation where admissible solutions are restricted to the rationals or the integers, or appropriate mathematical generalizations of such objects. The equations themselves tend to be polynomial, exponential, or a mixture of both, where variables in the ...