Some Generalized Formula For Sums of Cube

Abstract

The study of integer representations as a sum of powers is still a very long standing problem. In this work, the study of integer representation as a sum of cube is introduced and investigated for non-zero distinct integer solution. Let a1, a2, a3, · · · , an and d be any positive integers such that an − an−1 = an−1 − an−2 = · · · = a2 − a1 = d. This study formulates some general results for sums of n cube. In particular, this research introduces and develops the diophantine equation I = (a1 + a2 + a3 + · · · + an)L = a 3 1 + a 3 2 + a 3 3 + · · · + a 3 n for some integer L. The method involves decomposing integer I into sums of n cube and determination of general representation of integer L using case by case basis.