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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References:

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