# A Polynomial Taking Integer Values

by Robin Chapman (University of Exeter, UK)

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.)

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Capsule Course Topic(s):
Linear Algebra | Determinants