International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 42, Pages 2265-2268
On the ranges of discrete exponentials
1Department of Mathematics II, University Politechnica of Bucharest, Splaiul Independentei 313, Bucharest 77206, Romania
2Department of Mathematics, Ohio Northern University, Ada 45810, OH, USA
Received 3 December 2003
Copyright © 2004 Florin Caragiu and Mihai Caragiu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a fixed integer. We prove that there is no first-order formula in one free variable , written in the language of rings, such that for any prime with the set of all elements in the finite prime field satisfying coincides with the range of the discrete exponential function .