IIARD International Institute of Academic Research and Development

INTERNATIONAL JOURNAL OF APPLIED SCIENCES AND MATHEMATICAL THEORY (IJASMT )

E- ISSN 2489-009X
P- ISSN 2695-1908
VOL. 10 NO. 1 2024
DOI: https://doi.org/10.56201/ijasmt.v10.no1.2024.pg19.28

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

Marshal I. Sampson, Ekere Sunday Udofia,Christiana Igiri, Effiong, L.E., Eke N.

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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.

Coprime Integers, Divisibility, Euler Phi Function, Number Theory, Computational Illustration

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References:

1] Dash, D. K., & Wolu, N. (2020). On the Sum of Coprime Integers and Its Divisibility by
Certain Integers. Journal of Number Theory, 45(2), 123-135.

[2] Sampson M.I., Jackson Ante, Nduka Wonu (2020). On divisibility of Sum of Coprimes of
Integers by Integers and Primes. IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-
5728, p-ISSN: 2319-765X. Volume 17, Issue 1 Ser. III (Jan. – Feb. 2021), PP 39-49.
www.iosrjournals.org.

[3] Sampson M.I. (2023) Infinite Semigroups Whose Number of Independent Elements is Larger
than the Basis. IJRTI | Volume 8, Issue 7 | ISSN: 2456-3315.

[4] Sampson M.I., L. Zsolt, Achuobi J.O., Igiri C.F., Effiong L.E. (2023) On independence and
minimal generating set in semigroups and countable systems of semigroups. Intern…
[11:13 AM, 2/24/2024] +234 803 552 4502: References

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