Convergents of continued fractions and their application to diophantine equations (with computer program)

• Main Authors: Asuit, Floricel, Luis, Phillip Ortiz
• Format: text
• Language: English
• Published: Animo Repository 1994
• Subjects: Convergence; Fractions, Continued; Diophantine analysis; Programming (Mathematics); Numbers, Theory of; Equations > Numerical solutions
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16160
• Institution: De La Salle University

The study presents the theory of convergents of simple finite continued fractions and diophantine equations and the relationship between them. Convergents have their own unique patterns and are governed by certain theorems. The researchers present a method of solving linear diophantine equations using convergents based on the article of Joseph Holmes, entitled Continued Fractions.This study creates a pascal program that generates the convergents of a simple finite continued fraction and vice versa. Thus, given a linear diphantine equation, the program can be used to get a particular integral solution using the method of solution discussed in the paper.