Diophantine Equations

Saturdays from January 14-March 4

1:30 PM-3:00 PM PST/4:30 PM-6:00 PM EST

In this course, we will see a variety of methods for finding integer solutions to equations. Some of the topics covered include

• Linear Diophantine equations

• Pythagorean triples

• Fermat’s Last Theorem

• Exponential Diophantine equations

• Pell’s equations

• Elliptic curves

Lessons will be taught through Zoom. There will not be any homework, but I will give problems for students to think about and discuss between classes.

This class is intended primarily for advanced high school students, but students of any age are welcome to enroll.

Prerequisites:

• Algebra:

  • Factoring algebraic expressions

  • Finding roots of polynomials

  • Basic algebraic properties of complex numbers

• Number theory:

  • Prime factorizations

  • Euclidean algorithm

  • Modular arithmetic operations

  • Fermat’s little theorem/Euler’s theorem