Algebraic Method for Solving System of Linear Congruences

Authors

  • Polemer M. Cuarto Mindoro State College of Agriculture and Technology

DOI:

https://doi.org/10.32871/rmrj1503.01.07

Keywords:

Algebraic algorithm, system of linear congruences, Number Theory, Chinese Remainder Theorem, crypthography

Abstract

The paper aimed to devise an alternative algorithm for solving system of linear
congruences. This algorithm is an extension of the algebraic algorithm which is an alternative method for finding solutions in linear congruences. The basic idea of the technique is to convert the given linear congruences into linear equations and solve them algebraically. The advantage of this algorithm is the simplicity of its computations and its applicability to systems of linear congruences where the conditions of the Chinese Remainder Theorem that the moduli m1…mn should be pairwise coprime is not satisfied. Some illustrative examples are given to show validity of this method for solving system of linear congruences.

Author Biography

Polemer M. Cuarto, Mindoro State College of Agriculture and Technology

is a graduate of Bachelor of Secondary Education Major in Mathematics with magna cum laude honors and a graduate of Master of Arts in Education Major in Mathematics at Mindoro State College of Agriculture and Technology. He is a Ph.D. in Education Major in Mathematics candidate at the University of Batangas. Presently, he is a Mathematics Instructor of Mindoro State College of Agriculture and Technology Calapan City Campus. He is teaching major subjects such as Probability, Elementary and Advanced Statistics, Linear Algebra, Abstract Algebra, Mathematical Investigation and Modeling, and Problem Solving.

References

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Published

2015-06-30

How to Cite

Cuarto, P. M. (2015). Algebraic Method for Solving System of Linear Congruences. Recoletos Multidisciplinary Research Journal, 3(1). https://doi.org/10.32871/rmrj1503.01.07

Issue

Vol. 3 No. 1 (2015)

Section

Articles

License

Copyright of the Journal belongs to the University of San Jose-Recoletos