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
References
Srinivasarao BSS. A key exchange with Linear Diophantine equations. M.Phil., Dissertation;2020.
Deniz Yesilyurt. Solving Linear Diophantine Equations and Linear congruential Equations. Degree Project, Linnaeus University; 2012.
Roy UN, Sah RP, Sah AK, Sourabh SK. Linear Diophantine Equation: Solution and Applications. International Journal of Mathematics Trends and Technology (IJMTT). 2019;65(1).
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.
William J. Gilbert, Anu Pathria. Linear Diophantine equation; 1990.
Florentin Smarandache. Integer algorithms to solve Diophantine linear equations and systems. University of New Mexico, 200 College Road, Gallup, NM 87301, USA.
Tomas Hruz et Dominique Fortin. Parallelism in Hermite and Smith normal forms. Article;1994.
Arvind V. Linear Diophantine equation. Algebra and Computation Lecture note.
Deniz Yesilyurt. Solving Linear Diophantine Equations and Linear congruential Equations. Degree Project, Linnaeus University; 2012.
Roy UN, Sah RP, Sah AK, Sourabh SK. Linear Diophantine Equation: Solution and Applications. International Journal of Mathematics Trends and Technology (IJMTT). 2019;65(1).
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.
William J. Gilbert, Anu Pathria. Linear Diophantine equation; 1990.
Florentin Smarandache. Integer algorithms to solve Diophantine linear equations and systems. University of New Mexico, 200 College Road, Gallup, NM 87301, USA.
Tomas Hruz et Dominique Fortin. Parallelism in Hermite and Smith normal forms. Article;1994.
Arvind V. Linear Diophantine equation. Algebra and Computation Lecture note.
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