Assessing the Feasibility of Partitioning Squares of Consecutive Odd, Even, or All n Numbers into k Groups of Equal Sums: A Practical Computational Method and Theoretical Approach with Proofs

This repository contains the preprint article and the corresponding computational code for the topic: "Assessing the Feasibility of Partitioning Squares of Consecutive Odd, Even, or All n Numbers into k Groups of Equal Sums: A Practical Computational Method and Theoretical Approach with Proofs".

In 2 Version
"Added explanations and lemmas, and final proof at pages 29-30"

"Added explanations for mathematical Big(O) checking (especially for n * n / ln(n) instead of just n). Also added Big(O) logical version"

In 3 Version

"Added missing detail (case: p = 1) at page 24"

"Added some notes in lemma 2 at page 29, first lines of page 30"

"some punctuation and font corrections related to lemmas, at pages: 29-30"

In Version 4

"Added " | p = 2 or p = 1" in codes at pages: 4, 23, and 33"

"Fixed latex translation errors — Changed t * sk^2’s, and t  * sk’s, into t / sk^2’s ($\frac{t}{sk^2}$, "\frac{t}{sk^2}"), and t / sk’s ($\frac{t}{sk}$, "\frac{t}{sk}"); at pages: 2-3, and 31-32"

In Version 5

Changed $\frac{n  1}{2}$ (\frac{n  1}{2}) into $\frac{n + 1}{2}$ (\frac{n + 1}{2}), at page: 25