## STNB2020(34th edition)

### Automating the modular method for Frey Q-curves

#### Presenters

Joey van Langen

#### Abstract

The modular method has effectively been applied to solve a variety of
exponential Diophantine equations. Although the procedure is in
essence very similar for every case, only implementations for
particular Diophantine equations can be found in the literature. In
this talk I will describe the mathematical obstacles to generalizing
such approaches. The talk will focus on a general algorithm that can
be applied to problems for which a Frey Q-curve exists. An
implementation of this work in Sage provides a simple
way to obtain the results of the modular method for such problems. As
an illustration we will use this approach on the Diophantine equation
$(x - y)^4 + x^4 + (x + y)^4 = z^l$.

#### Files

No files available for download