A Clean Approach to Rational Cubic Residues
| dc.creator | Vandervelde, Sam | |
| dc.date | 2006-11-06 | |
| dc.date | 2007-06-11 | |
| dc.date.accessioned | 2026-07-07T08:04:45Z | |
| dc.date.available | 2026-07-07T08:04:45Z | |
| dc.description | 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=(3^19+5^82)/4, a question which is essentially impossible to answer with Lehmer's original criterion. | |
| dc.description | 15 pages, submitted to International Journal of Number Theory, one paragraph appended to section five in v2 | |
| dc.identifier | https://arxiv.org/abs/math/0611151 | |
| dc.identifier | http://arxiv.org/abs/math/0611151 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130080 | |
| dc.subject | Number Theory | |
| dc.subject | 11A15 | |
| dc.title | A Clean Approach to Rational Cubic Residues | |
| dc.type | text |