Natural solutions of Diophantine linear equation with n unknowns

Article type: Research Article

Authors: Mestechkin, M.M.

Affiliations: 12772 Seabreeze Farms Dr. Apt 33, San Diego, CA 92130, USA. E-mail: [email protected]

Abstract: A general solution, containing n-1 arbitrary integers, of linear Diophantine equation with n unknowns is presented in terms of parameters of n-1 Euclidean algorithms. Construction procedures of general and natural solutions based on application of ``truncated'' parameters of Euclidean algorithms are described. Domains of equation right-hand part values guaranteeing existence of a given number of natural solutions are found. Explicit formulae for natural solutions are presented. Some illustrations are given.

Keywords: Diophantine linear equation, natural solutions

DOI: 10.3233/JCM-150591

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 16, no. 1, pp. 175-184, 2016