Parametric Solutions of System of Linear Diophantine Equations by Crushing Method
Asian Research Journal of Mathematics,
Page 48-56
DOI:
10.9734/arjom/2021/v17i930330
Abstract
There are studies on parametric solutions of system of Linear Diophantine equations based on uni-modular reductions of the coefficient matrix. In this paper we generate parametric solutions, with uni-modular row reductions on the coefficient matrix, based on the steps used in obtaining gcd of the coefficients in a row by crushing method. This application of gcd by crushing specifies an order for the row reductions and enables to give algorithm for the computations.
Keywords:
- Diophantine equations
- parametric solutions
How to Cite
Kameswari, P. A., & Belay, A. (2021). Parametric Solutions of System of Linear Diophantine Equations by Crushing Method. Asian Research Journal of Mathematics, 17(9), 48-56. https://doi.org/10.9734/arjom/2021/v17i930330
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Sagar Panda. Diophantine equation. National Institute of Technology Rourkela Rourkela, Orissa-769008; 2011.
Felix Lasebnik. On systems of Linear Diophantine equation. 1996;69(4):261-266.
Azam A. Imomov, Yorqin T. Khodjaev. On some methods for solution of Linear Diophantine equation; 2019.
James Mcivor. Lecture notes on Diophantine Equations; 2012.
Vasilious Evangelos Tourloupis. Hermite Normal Forms and its cryptographic applications. University of Wollongong Thesis Collection; 2013.
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