Solutions to systems of linear congruences

Date of Publication

1993

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Abstract/Summary

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.

Abstract Format

html

Language

English

Format

Print

Accession Number

TU06295

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Physical Description

89 leaves

Keywords

Congruences (Geometry); Numbers, Theory of; Linear systems; Programming (Mathematics)

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