Equations in Number Theory

This course was written in collaboration with Andrea Marino, a two-time math olympiad gold medalist and mathematics PhD at Tor Vergata University.

In this course, you'll learn one of the most fundamental techniques in number theory: solving Diophantine (integer) equations. You'll apply these techniques to both abstract problems, as well as to problems in chemistry, geometry, game theory, and billiards.

• Introduction:
• Thinking Discrete: A fundamental tool in number theory involves solving equations where integer solutions are needed.
• Foundations:
• Linear Equations: adding descriptions correction
• Bezout and Billiards: Predict the path of a billiard ball using linear equations.
• Modular Arithmetic: The mod operation is part of every number theorist's toolbox.