Solvability of ternary equations of signature (3,3,2)

In this thesis we examine the primitive solvability of Diophantine equations of the form ax^3 + by^3 = cz^2. For square-free a, b, c, we identify various criteria necessary for the existence of primitive solutions, including a sufficient one. We also present a relatively efficient algorithm to determine whether this criterion is satisfied. Using the algorithm, we compute some data on the relative distribution of the occurrence of various obstructions to the existence of primitive solutions.