Abstract

<p>Coprime integers—pairs of integers with no common positive divisors other than 1—form a foundational concept in number theory with wide-ranging applications in areas such as cryptography, algebra, and computational mathematics. This study explores the divisibility properties of coprime integers, building upon the theoretical framework introduced by Dash and Wolu (2020), who examined conditions under which the sum of coprime integers is divisible by a given integer. We aim to deepen the understanding of these divisibility patterns through a combined theoretical and computational approach. Key focus areas include identifying structural relationships within coprime sets, analyzing how arithmetic functions interact with coprime conditions, and investigating potential generalizations for multiple integers. The study also implements algorithmic simulations to validate theoretical claims and explore divisibility behavior across large data sets. Our findings reveal nuanced patterns in divisibility among coprime integers, contributing to ongoing discourse in discrete mathematics and expanding the scope for future research in both pure and applied mathematical contexts.</p>