Optical solutions for linear Diophantine equations

Determining whether a Diophantine equation has a solution or not is the most important challenge in solving this type of problems. In this paper a special computational device which uses light rays is proposed to answer this question, namely check the existence of nonnegative solutions for linear Di...

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Bibliographic Details
Published in:Journal of Optoelectronics and Advanced Materials 2009-11, Vol.11 (11), p.1728-1734
Main Authors: Muntean, O, Oltean, M
Format: Article
Language:English
Online Access:Get full text
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Summary:Determining whether a Diophantine equation has a solution or not is the most important challenge in solving this type of problems. In this paper a special computational device which uses light rays is proposed to answer this question, namely check the existence of nonnegative solutions for linear Diophantine equations. The way of representation for this device is similar to an directed graph, having a number of nodes equal to the number of variables of the equation plus the destination node. The arcs connecting these nodes have assigned a number (length) which corresponds to coefficients of the equation or it is a predefined constant. The light traversing the device follows all possible routes. In each arc it will be delayed by an amount of time indicated by the length of that arc. At the destination node, if a light ray arrives at the moment equal to the free term of the equation plus some constants we may infer that the equation has solution, otherwise it has not.
ISSN:1454-4164