An elementary method of solving certain Diophantine equations

摘要

This paper provides an elementary method of obtaining the complete solution of certain homogeneous diophantine equations of the type f(s_1,x_2, …,x_n) = cy~k where f(x_i) is an integral form of degree k in the variables x_i, i = 1,2,…,n. When f(x_i) is a form in three variables, all non-trivial fourth and fifth degree equations solvable by this method have been enumerated.