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STNB2020(34th edition)

A modular approach to Fermat equations of signature (p,p,5) using Frey hyperelliptic curves

Presenters

Imin Chen

Abstract

We will explain how the ideas and methods developed in previous lectures can be continued to study Fermat type equations of signature (p,p,5) in joint work with Angelos Koutsianas. Specifically, we will give a resolution of the equation xn+yn=z5 in the congruence classes mod 10 which avoid the trivial solutions. The approach uses two Frey hyperelliptic curves of genus 2 introduced by Darmon, ideas from his program, and extensions of the methods described in the previous two lectures.

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