Farey sequences and linear diophantine equations

• Main Authors: Bautista, Peter Anthony D., Padilla, John Michael C.
• Format: text
• Language: English
• Published: Animo Repository 1993
• Subjects: Series, Farey; Diophantine analysis; Equations; Numbers, Theory of; Farey sequences
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16116
• Institution: De La Salle University

This thesis introduces the concept of using Farey Sequence in obtaining particular solutions of Linear Diophantine Equations in two unknowns. The relationship between the mediant and adjacent Farey Fractions is shown.The thesis itself is based on the article by T.E. Kriewall regarding Mckay's Theorem and Farey sequences. However, Kriewall restricted himself to the use of only the left adjacent Farey Fraction. The researchers presented the use of the other fraction in the quest for a solution to the equation.Furthermore, the researchers incorporated the principles stated by Kriewall into a program written in Turbo Pascal whose sole purpose is to determine the solutions to a given Linear Diophantine Equation.