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Spring 1980 On a problem suggested by Olga Taussky-Todd
Morris Newman
Illinois J. Math. 24(1): 156-158 (Spring 1980). DOI: 10.1215/ijm/1256047802

Abstract

The problem considered is to characterize those integers $m$ such that $m = \mathrm{det}(C)$, $C$ an integral $n \times n$ circulant. It is shown that if $(m,n) = 1$ then such circulants always exist, and if $(m,n)> 1$ and $p$ is a prime dividing $(m,n)$ such that $p^{t}||n$, then $p^{t+1}|m$. This implies for example, that $n$ never occurs as the determinant of an integral $n \times n$ circulant, if $n > 1$.

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Morris Newman. "On a problem suggested by Olga Taussky-Todd." Illinois J. Math. 24 (1) 156 - 158, Spring 1980. https://doi.org/10.1215/ijm/1256047802

Information

Published: Spring 1980
First available in Project Euclid: 20 October 2009

zbMATH: 0414.15007
MathSciNet: MR550657
Digital Object Identifier: 10.1215/ijm/1256047802

Subjects:
Primary: 15A36
Secondary: 15A15, 15A57

Rights: Copyright © 1980 University of Illinois at Urbana-Champaign

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Vol.24 • No. 1 • Spring 1980
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