2006/11/06 by Sam Vandervelde, Vandervelde, Sam
Computer Science · Mathematics · #11A15 #Algebraic Geometry and Number Theory #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A15
paper · pdf · doi:10.48550/arxiv.math/0611151
15 pages, submitted to International Journal of Number Theory, one paragraph appended to section five in v2
openalex publication_date 2006/11/06 · arxiv created 2007/06/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1958 E. Lehmer found an explicit description of those primes p for which a given prime q is a cubic residue. In this paper we demonstrate that a similar result may be obtained for cubic nonresidues, yielding a cubic character for fixed p that provides an effective means for ascertaining whether or not an arbitrary integer c is a cubic residue modulo p. As an illustration of this technique, we determine whether 1982 is a cubic residue modulo the 131-digit prime p=(319+582)/4, a question which is essentially impossible to answer with Lehmer's original criterion.