This paper explores the π Γ π Mersenne power GCD matrices defined on sets of positive integers, focusing on factor-closed and gcd-closed sets. By employing the form π(π‘π ,π‘π) = 2 (π‘π ,π‘π ) β 1, we investigate the π π‘β power Mersenne GCD matrix (ππ ) 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.
No takes yet. Share an insight, caveat, or question.
Awad et al. (2024) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: