Samir Siksek

collaborators

2 papers

math.NT2024

The modular approach to Diophantine equations over totally real fields

Maleeha Khawaja, Samir Siksek

Wiles' proof of Fermat's last theorem initiated a powerful new approach towards the resolution of certain Diophantine equations over $Q$ . Numerous novel obstacles arise wh…

math.NT2016

On powers that are sums of consecutive like powers

Vandita Patel, Samir Siksek

Let $k \geq 2$ be even, and let $r$ be a non-zero integer. We show that for almost all $d \geq 2$ (in the sense of natural density), the equation $$ x^k+(x+r)^k+\cdots+(x+(d-1)r)^k=y…