41 citations · 198 across the 39 of their papers we have counts for
6 papers · 1 filter
Rational Points on Erdos-Selfridge Superelliptic Curves
Michael Bennett, Samir Siksek
Given , we show that there are at most finitely many rational numbers and and integers (with ) for which $$ x (x+1) \cdo…
Superelliptic equations arising from sums of consecutive powers
Michael A. Bennett, Vandita Patel, Samir Siksek
Using only elementary arguments, Cassels solved the Diophantine equation in integers , . The generalization (with , …
Residual Representations of Semistable Principally Polarized Abelian Varieties
Samuele Anni, Pedro Lemos, Samir Siksek
Let be a semistable principally polarized abelian variety of dimension defined over the rationals. Let be a prime and let $\barρ_{A,\ell} : G_{\mathbb{Q}} \rightarro…
Modular elliptic curves over real abelian fields and the generalized Fermat equation
Samuele Anni, Samir Siksek
Using a combination of several powerful modularity theorems and class field theory we derive a new modularity theorem for semistable elliptic curves over certain real abelian field…
Squares in arithmetic progression over cubic fields
Andrew Bremner, Samir Siksek
Euler showed that there can be no more than three integer squares in arithmetic progression. In quadratic number fields, Xarles has shown that there can be arithmetic progressions…
Every integer greater than 454 is the sum of at most seven positive cubes
Samir Siksek
A long-standing conjecture states that every positive integer other than 15, 22, 23, 50, 114, 167, 175, 186, 212, 231, 238, 239, 303, 364, 420, 428, 454 is a sum of at most seven p…