International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2004 / Article

Open Access

Volume 2004 |Article ID 634790 | https://doi.org/10.1155/S0161171204312056

Florin Caragiu, Mihai Caragiu, "On the ranges of discrete exponentials", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 634790, 4 pages, 2004. https://doi.org/10.1155/S0161171204312056

On the ranges of discrete exponentials

Received03 Dec 2003

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 tat(modp).

Copyright © 2004 Hindawi Publishing Corporation. 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.


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