On Generalized Sums of Six, Seven and Nine Cube

Boaz Simatwo Kimtai; Lao Hussein Mude

doi:10.51867/scimundi.3.1.14

Authors

Boaz Simatwo Kimtai Department of Mathematics and Actuarial Science, Kisii University, P. O. Box 408-40200, Kisii, Kenya https://orcid.org/0000-0002-1314-6119
Lao Hussein Mude Department of Pure and Applied Sciences, Kirinyaga University, P. O. Box 143-10300, Kerugoya, Kenya

DOI:

https://doi.org/10.51867/scimundi.3.1.14

Keywords:

Diophantine Equation, Sums of Six, Seven and Nine Cube

Abstract

Let u₁, u₂, u₃,・・・ u_n be integers such that u_n − u_n−1 = u_n−1 − u_n−2 = ・・・ = a₂ − a₁ = d. In this article, the study of sums of cube in arithmetic progression is discussed. In particular, the study develops and introduces some generalized results on sums of six, seven and nine cube for any arbitrary integers in arithmetic sequences. The method of study involves analogy grounded on integer decomposition and factorization. The result in this study will prove the existing results on sums of cubes.

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