Solutions to systems of linear congruences

• Main Authors: Villareal, Maria Gracia T., Velarde, Rommel Jonathan T.
• Format: text
• Language: English
• Published: Animo Repository 1993
• Subjects: Congruences (Geometry); Numbers, Theory of; Linear systems; Programming (Mathematics)
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16122
• Institution: De La Salle University

This thesis presents solutions to two forms of systems of linear congruences. The first form consists of n linear congruences with n unknowns, and with a single modulo. This is solved through the use of matrices. However, this thesis covers only such forms having the determinants of the coefficient matrix and the modulo relatively prime. The second form consists of one unknown and different moduli, and where the moduli are relatively prime. This is solved through the use of the Chinese Remainder Theorem.All theorems and definitions were consulted from books, with Kenneth H. Rosen's Elementary Number Theory and its Applications and Anthony J. Pettofrezzo and Daniel R. Byrkit's Elements of Number Theory providing the bulk of the concepts. The researchers combined the ideas of the two books to generate a comprehensive result of the study.Furthermore, the researchers provided a software package to solve for the solutions to systems of linear congruences. This was done through programming using Turbo Pascal 6.0.