On the Solvability of Quintic and Sextic Diophantine Equations of the Type f(x, y)=f(u, v) Original Research Article

In this paper theorems have been obtained giving necessary and sufficient conditions for the solvability of the diophantine equations f(x, y)=f(u, v) where f(x, y) is an arbitrary binary quintic or sextic form. These theorems have then been applied to obtain numerical or parametric solutions of certain specific quintic and sextic equations.