An octic diophantine equation and related families of elliptic curves

Ajai Choudhry, Arman Shamsi Zargar

We obtain two parametric solutions of the diophantine equation $\varphi (x_1,x_2,x_3)=\varphi (y_1,y_2,y_3)$ where $\varphi (x_1,x_2,x_3)$ is the octic form defined by $ϕ(x_1, x_2, x_3)=x_1^8+ x_…