On Mersenne Power GCD Matrices

Yahia Awad; Ragheb Mghames; Karim Amin

doi:10.55549/epstem.1520652

EN

On Mersenne Power GCD Matrices

Abstract

This paper explores the 𝑛 × 𝑛 Mersenne power GCD matrices defined on sets of positive integers, focusing on factor-closed and gcd-closed sets. By employing the form 𝑓(𝑡𝑖 ,𝑡𝑗) = 2 (𝑡𝑖 ,𝑡𝑗 ) − 1, we investigate the 𝑟 𝑡ℎ power Mersenne GCD matrix (𝑀𝑟 ) and provide comprehensive insights into its factorizations, determinants, reciprocals, and inverses. Building upon previous research, particularly Chun's work on power GCD matrices, we extend the analysis to Mersenne numbers, offering a thorough understanding of their properties. The study contributes to the broader understanding of arithmetic functions and their applications in matrix theory.

Keywords

References

Awad, Y., Mghames, R., & Amin, K. (2024). On mersenne power GCD matrices. The Eurasia Proceedings of Science, Technology, Engineering & Mathematics (EPSTEM), 28, 224-233.

Details

Primary Language

English

Subjects

Software Engineering (Other)

Journal Section

Conference Paper

Authors

Yahia Awad This is me
Lebanon

Ragheb Mghames This is me
Lebanon

Karim Amin This is me
Lebanon

Early Pub Date

July 22, 2024

Publication Date

August 1, 2024

Submission Date

February 5, 2024

Acceptance Date

April 17, 2024

Published in Issue

Year 2024 Volume: 28

DOI

https://doi.org/10.55549/epstem.1520652

IZ

https://izlik.org/JA54RR57ZE

Cite

RIS / Bibtex

APA

Awad, Y., Mghames, R., & Amin, K. (2024). On Mersenne Power GCD Matrices. The Eurasia Proceedings of Science Technology Engineering and Mathematics, 28, 224-233. https://doi.org/10.55549/epstem.1520652

AMA

1.Awad Y, Mghames R, Amin K. On Mersenne Power GCD Matrices. EPSTEM. 2024;28:224-233. doi:10.55549/epstem.1520652

Chicago

Awad, Yahia, Ragheb Mghames, and Karim Amin. 2024. “On Mersenne Power GCD Matrices”. The Eurasia Proceedings of Science Technology Engineering and Mathematics 28 (August): 224-33. https://doi.org/10.55549/epstem.1520652.

EndNote

Awad Y, Mghames R, Amin K (August 1, 2024) On Mersenne Power GCD Matrices. The Eurasia Proceedings of Science Technology Engineering and Mathematics 28 224–233.

IEEE

[1]Y. Awad, R. Mghames, and K. Amin, “On Mersenne Power GCD Matrices”, EPSTEM, vol. 28, pp. 224–233, Aug. 2024, doi: 10.55549/epstem.1520652.

ISNAD

Awad, Yahia - Mghames, Ragheb - Amin, Karim. “On Mersenne Power GCD Matrices”. The Eurasia Proceedings of Science Technology Engineering and Mathematics 28 (August 1, 2024): 224-233. https://doi.org/10.55549/epstem.1520652.

JAMA

1.Awad Y, Mghames R, Amin K. On Mersenne Power GCD Matrices. EPSTEM. 2024;28:224–233.

MLA

Awad, Yahia, et al. “On Mersenne Power GCD Matrices”. The Eurasia Proceedings of Science Technology Engineering and Mathematics, vol. 28, Aug. 2024, pp. 224-33, doi:10.55549/epstem.1520652.

Vancouver

1.Yahia Awad, Ragheb Mghames, Karim Amin. On Mersenne Power GCD Matrices. EPSTEM. 2024 Aug. 1;28:224-33. doi:10.55549/epstem.1520652