## Illinois Journal of Mathematics

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

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

#### 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

**Permanent link to this document**

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