On Mersenne Power GCD Matrices

Year 2024, Volume: 28, 224 - 233, 01.08.2024

Yahia Awad Ragheb Mghames Karim Amin

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

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

Power GCD Matrix , Factor-closed sets , GCD-closed sets , Mersenne numbers

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.