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Research Article Open access CC BY 4.0

Some Generalized Formula For Sums of Cube

Lao Hussein Mude, Zachary Kaunda Kayiita, Kinyanjui Jeremiah Ndung'u

Journal of Advances in Mathematics and Computer Science · pp. 47–52 · Published 17 Jun 2023

10.9734/jamcs/2023/v38i81789

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 \(a_1\), \(a_2\), \(a_3\), ... , \(a_n\)  and d be any positive integers such that \(a_n\) - \(a_n\)-1= \(a_n\)-1 - \(a_n\)-2 = ... = \(a_2\) - \(a_1\) = d. This study formulates some general results for sums of n cube. In particular, this research introduces and develops the diophantine equation I =(\(a_1\)+\(a_2\)+\(a_3\)+...+\(a_n\)) L = \(a_1^3\)+\(a_2^3\)+\(a_3^3\)+...+\(a_n^3\) 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.

Diophantine equation sums of cube decomposition integer

Cited by 6

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