Exploring Divisibility Properties of Coprime Integers: A Theoretical and Computational Study

Abstract

This research investigates the divisibility properties of coprime integers, building upon the foundational work of Dillip Kumar Dash and Nduka Wolu (2020) regarding the sum of coprime integers and its divisibility by certain integers. While Dash and Wolu established a result concerning the divisibility of the sum of coprime integers byan integer, we provide the converse of this result, revealing insights into the relationship between prime integers and the divisibility of coprime integer sums. Our study introduces a generalized property of integers that underpins these divisibility properties and provides a theoretical framework for understanding the phenomenon. Additionally, we present a computational illustration for generating coprime integers to test our theoretical findings, offering practical insights into the validity of our results. The research contributes to the understanding of the arithmetic properties of coprime integers and their implications for number theory.

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