Equal sums of like powers

This paper is concerned with four diophantine systems, namely, (i) Sigma (4 )(i=1) x(i)(k) = Sigma (4)(i=1) y(i)(k), k = 1, 2, 4; (ii) Sigma (4)(i=1) x (i)(k) = Sigma (4)(i=1) y(i)(k), k = 1, 3, 4. (iii) Sigma (4)(i=1) x(i)(k) = Sigma (4)(i=1) y(i)(k), k = 2, 3, 4; (iv) Sigma (3)(i=1) x(i)(k) = Sigma (3)(i=1) y(i)(k), k = 2, 3, 4. Parametric solutions as well as numerical ex amples of solutions in positive integers of the first three diophantine sys tems have been obtained in the paper. For the fourth diophantine system, so lutions do not exist in positive real numbers and a single numerical soluti on in integers has been obtained.