Non-trivial Solutions of $A{a}^p+B{b}^p=C{c}^3$ over Number Fields

Yasemin Kara, Stef Nomden, Ekin Özman

In this paper, we investigate solutions to the Diophantine equation $A{a}^p+B{b}^p=C{c}^3$ over number fields using the modular method. Assuming certain standard modularity conj…