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Article Dans Une Revue The American Mathematical Monthly Année : 2016

## What You Should Know About Integer-Valued Polynomials

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Paul-Jean Cahen
• Fonction : Auteur
Jean-Luc Chabert

#### Résumé

The authors wish to celebrate the centenary of Polya's paper Ueber ganzwertige ganze funktionen where first explicitly appeared the term integer-valued polynomials.'' This survey is focused on the emblematic example of the ring Int(Z) formed by the polynomials with rational coefficients taking integer values on the integers. This ring has surprising algebraic properties, often obtained by means of analytical properties. Yet, the article mentions also several extensions, either by considering integer-valued polynomials on a subset of Z, or by replacing Z by the ring of integers of a number field.

#### Domaines

Mathématiques [math]

### Dates et versions

hal-03621215 , version 1 (28-03-2022)

### Identifiants

• HAL Id : hal-03621215 , version 1
• DOI :

### Citer

Paul-Jean Cahen, Jean-Luc Chabert. What You Should Know About Integer-Valued Polynomials. The American Mathematical Monthly, 2016, 123 (4), pp.311-337. ⟨10.4169/amer.math.monthly.123.4.311⟩. ⟨hal-03621215⟩

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