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Une Caractérisation des Polynômes Prenant des Valeurs Entières Sur Tous les Nombres Premiers

Published online by Cambridge University Press:  20 November 2018

Jean-Luc Chabert
Jean-Luc Chabert*
Affiliation:
Département de Mathématiques, Institut Supérieur des Sciences et Techniques de St. Quentin Université de Picardie 48, rue Raspail 02109 St. Quentin, France, e-mail: jean-luc.chabert@u-picardie.fr
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Abstract

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We give a characterization of polynomials with rational coefficients which take integral values on the prime numbers: to test a polynomial of degree n, it is enough to consider its values on the integers from 1 to 2n —1.

Résumé

Résumé

Nous donnons une caractérisation des polynômes à coefficients rationnels prenant des valeurs entières sur tous les nombres premiers: pour tester un polynôme donné de degré n, il suffit de considérer ses valeurs sur les entiers de 1 à 2n — 1.

Keywords

11C0811A4111Y16
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 4 , 01 December 1996 , pp. 402 - 407
Copyright
Copyright © Canadian Mathematical Society 1996

References

1. Cahen, R-J., Integral-valued polynomials on a subset, Proc. Amer. Math. Soc. 117(1993), 919–929.Google Scholar
2. Chabert, J.-L., Chapman, S., Smith, W., A basis for the ring of polynomials integer-valued on prime numbers, à paraître.Google Scholar
3. Gilmer, R., Sets that determine integer-valued polynomials, J. Number Theory 33(1989), 95–100.Google Scholar
4. Ostrowski, A., Ueber ganzwertige Polynôme in algebraischen Zahlkôrpem, J. Reine Angew. Math. 149 (1919), 117–124.Google Scholar
5. Pôlya, G., Ueber ganzwertige Polynôme in algebraischen Zahlkôrpem, J. Reine Angew. Math. 149(1919), 97–116.Google Scholar