  Historically in math literature there are instances where solutions have been
arrived at by different authors for equation 1 for six powers on both side of
equation, for different degree 2,3,4,5,6,7,8,9. See reference number 1, by A.
Bremner & J. Delorme and reference number 10, by Tito Piezas. The difference is
that this paper has done systematic analysis of equation 1. While numerical
solutions for equation 1, is available on Wolfram math website, search for
parametric solutions to equation 1, in various publications for all degree
2,3,4,5,6,7,8,9 did not yield results. The authors of this paper have selected
six terms on each side of equation 1, since the difficulty of the problem
increases every time a term is deleted on each side of equation 1. The authors
have provided parametric solutions for equation 1, for degree 2, 3, 4, 5 & 6
and for degree 7, 8 & 9 solutions using elliptical curve method has been
provided. Also we would like to mention that solutions for degree 7, 8 & 9
using elliptic curve method has infinite numerical solutions. Keywords, Pure
math, Diophantine equations, Equal sums, parameteric equations.
