Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-27T09:09:11.750Z Has data issue: false hasContentIssue false
  • English
  • Français

Proof of a Conjecture of Chowla and Zassenhaus on Permutation Polynomials

Published online by Cambridge University Press:  20 November 2018

Stephen D. Cohen
Stephen D. Cohen*
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The following conjecture of Chowla and Zassenhaus ( 1968) is proved. If f(x) is an integral polynomial of degree ≧ 2 and p is a sufficiently large prime for which f (considered modulo p) is a permutation polynomial of the finite prime field Fp, then for no integer c with 1 ≦ c < p is f(x) + cx a permutation polynomial of Fp.

Keywords

12C05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 2 , 01 June 1990 , pp. 230 - 234
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Chowla, S. and Zassenhaus, H., Some conjectures concerning finite fields, Norske Vid. Selsk. Forh. (Trondheim), 41 (1968), 34–35.Google Scholar
2. Fried, M., On a conjecture of Schur, Michigan Math. J., 17 (1970), 41–55.Google Scholar
3. Lidl, R. and Mullen, G. L., When does a polynomial over a finite field permute the elements of the field?, Amer. Math. Monthly, 95 (1988), 243–246.Google Scholar
4. Lidl, R. and Niederreiter, H., Finite fields, Encyclopaedia of Math, and its Appl., vol. 20, Addison- Wesley, Reading, Mass., 1983.Google Scholar
5. Mullen, G. L. and Niederreiter, H., Dickson polynomials over finite fields and complete mappings, Canad. Math. Bull., 30 (1987), 19–27.Google Scholar
6. Niederreiter, H. and Robinson, K. H., Complete mappings of finite fields, J. Austral. Math. Soc, Ser. A, 33 (1982), 197–212.Google Scholar
7. Turnwald, G., On a problem concerning permutation polynomials, Trans. Amer. Math. Soc, 302 (1987), 251–267.Google Scholar
8. Wan, Daqing, Permutation polynomials over finite fields, Acta. Math. Sinica, New Series, 3 (1987), 1–5.Google Scholar