Ashleigh Wilcox

A systematic approach to solving Diophantine equations

This talk reports on the following project: define a suitable notion of "size'' of a polynomial Diophantine equation, order all equations by size, and solve them in this order. On the way, we discuss how to solve Diophantine equations using Vieta jumping, Jacobi symbols, the Mordell-Weil sieve, develop a general method to solve all two-variable three-monomial equations, and deduce the complete list of integers |n| ≤ 200 which are representable as the difference of two fourth powers.