Greatest common divisor matrices. (English) Zbl 0672.15005
Authors’ summary: Let \(S=\{x_ 1,x_ 2,...,x_ n\}\) be a set of distinct positive integers. The \(n\times n\) matrix \([S]=(s_{ij}),\) where \(s_{ij}=(x_ i,x_ j),\) the greatest common divisor of \(x_ i\) and \(x_ j\), is called the greatest common divisor (GCD) matrix of S. The paper studies the GCD matrices in the direction of their structure, determinant, and arithmetic in \(Z_ n\). Several open problems are posed.
Reviewer: R.Covaci
MSC:
| 15B36 | Matrices of integers |
| 15A15 | Determinants, permanents, traces, other special matrix functions |
| 11C20 | Matrices, determinants in number theory |
| 11A05 | Multiplicative structure; Euclidean algorithm; greatest common divisors |
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