On the ranges of discrete exponentials

Florin Caragiu and Mihai Caragiu

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-4

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 F p satisfying ϕ coincides with the range of the discrete exponential function t ↦ a t ( mod p ) .

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:634790

DOI: 10.1155/S0161171204312056

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