Integral points on hyperelliptic curves

Abstract: I will report on joint work with Yann Bugeaud, Maurice Mignotte, Samir Siksek and Szabolcs Tengely on a new method to determine all integral solutions to an equation of the form y² = f(x). One ingredient is an astronomical, but reasonable and computable bound on |x|, the other is a sieving procedure using the group of rational points on the Jacobian variety of the curve. I will illustrate this approach by solving the binomial coefficient equation \binom{y}{2} = \binom{x}{5}.