Solving equations of signature $(p,p,2)$ with coefficients over number fields

Begum Gulsah Cakti, Erman Isik, Yasemin Kara +1

Using the modular method, we study solutions to the Diophantine equation $$A{a}^p+B{b}^p=C{c}^2$$ over number fields. We first prove an asymptotic result for general number fields satisf…