## Illinois Journal of Mathematics

### On a problem suggested by Olga Taussky-Todd

Morris Newman

#### 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 $n > 1$.

#### Article information

Source
Illinois J. Math., Volume 24, Issue 1 (1980), 156-158.

Dates
First available in Project Euclid: 20 October 2009

https://projecteuclid.org/euclid.ijm/1256047802

Digital Object Identifier
doi:10.1215/ijm/1256047802

Mathematical Reviews number (MathSciNet)
MR550657

Zentralblatt MATH identifier
0414.15007

Subjects
Primary: 15A36
Secondary: 15A15: Determinants, permanents, other special matrix functions [See also 19B10, 19B14] 15A57

#### Citation

Newman, Morris. On a problem suggested by Olga Taussky-Todd. Illinois J. Math. 24 (1980), no. 1, 156--158. doi:10.1215/ijm/1256047802. https://projecteuclid.org/euclid.ijm/1256047802