International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 41-44, Pages 2265-2268
doi:10.1155/S0161171204312056
On the ranges of discrete exponentials
Florin Caragiu1
and Mihai Caragiu2
1Department of Mathematics II, University Politechnica of Bucharest, Splaiul Independentei 313, Bucharest 77206, Romania
2Department of Mathematics, Ohio Northern University, Ada 45810, OH, USA
Abstract
Let a>1 be a fixed integer. We prove that there is no first-order formula ϕ(X) in one free variable X, written in the language of rings, such that for any prime p with gcd(a,p)=1 the set of all elements in the finite prime field Fp satisfying ϕ coincides with the range of the discrete exponential function t↦at(modp).