Methods for arriving at numerical solutions for equations of the type [k+3] and [k+5] biquadratics equal to a bi-quadratic for different values of k

Abstract: Different authors have done analysis regarding sums of powers References number 1,2 and 3, but systematic approach for solving Diophantine equations having sums of many biquadratics equal to a quartic has not been done before. In this paper we give methods for finding numerical solutions to equation A given above in section one. Next in section two, we give methods for finding numerical solutions for equation B given above. As is known that finding parametric solutions to biquadratic equations is not easy by conventional method. So the authors have found numerical solutions to equation A and B using elliptic curve theory.