Finding integer solutions to an equation may seem quite trivial at first glance, but behind seemingly 'simple' equations lies some of the deepest mathematics known to number theorists. We outline some techniques used via the study of the equation $F_n + 2 = y^p$. This is joint work with Michael Bennett (University of British Colombia) and Samir Siksek (University of Warwick). We then move off towards explicit calculations and have a look at some interesting graphs arising from studying congruences between newforms. This part is joint work with Samuele Anni (Aix Marseille Université).

The Postdocs Seminar is a series of informal talks by Postdoctoral fellows. The aim is to learn some basics about each others research areas and to get into contact.