#### Vol. 15, No. 1, 1965

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On arithmetic properties of coefficients of rational functions

### David Geoffrey Cantor

Vol. 15 (1965), No. 1, 55–58
##### Abstract

The purpose of this note is to prove the following generalization of a result of Polya:

Theorem. Let $\left\{{a}_{n}\right\}$ be a sequence of algebraic integers, and $f$ a nonzero polynomial with complex coefficients. If ${\sum }_{n=0}^{\infty }f\left(n\right){a}_{n}{z}^{n}$ is a rational function, then so is ${\sum }_{n=0}^{\infty }{a}_{n}{z}^{n}$.

Primary: 12.30
Secondary: 10.76