On a class of generalized Fermat equations of signature $(2,2n,3)$

Karolina Chałupka, Andrzej Dąbrowski, Gökhan Soydan

We consider the Diophantine equation $7x^2+y^{2n}=4z^3$. We determine all solutions to this equation for $n=2,3,4$ and $5$. We formulate a Kraus type criterion for show…