You are here

A Polynomial Taking Integer Values

by Robin Chapman (University of Exeter, UK)

This article originally appeared in:
Mathematics Magazine
April, 1996

Subject classification(s): Linear Algebra
Applicable Course(s): 3.8 Linear/Matrix Algebra

The article supplies a short, elementary proof that for integers \(a_1 < a_2 < \cdots < a_n \), the expression \( \prod_{n \geq i > j \geq 1} \frac{a_i - a_j}{i-j} \) is an integer.  This previously known result is proved using the Vandermonde determinant.  (Please note a typo in the first sentence of the paper where a fraction bar has been omitted.)

A pdf copy of the article can be viewed by clicking below. Since the copy is a faithful reproduction of the actual journal pages, the article may not begin at the top of the first page.

To open this file please click here.

These pdf files are furnished by JSTOR.

Classroom Capsules would not be possible without the contribution of JSTOR.

JSTOR provides online access to pdf copies of 512 journals, including all three print journals of the Mathematical Association of America: The American Mathematical Monthly, College Mathematics Journal, and Mathematics Magazine. We are grateful for JSTOR's cooperation in providing the pdf pages that we are using for Classroom Capsules.

Capsule Course Topic(s):
Linear Algebra | Determinants
Average: 2.8 (13 votes)