On a distribution property of the residual order of a (mod p)
| dc.creator | Chinen, K. | |
| dc.creator | Murata, L. | |
| dc.date | 2002-11-05 | |
| dc.date.accessioned | 2026-07-07T04:52:40Z | |
| dc.date.available | 2026-07-07T04:52:40Z | |
| dc.description | Let a be a positive integer greater than 1, and Q_a(x;k,j) be the set of primes p less than x such that the residual order of a(mod p) is congruent to j modulo k. In this paper, the natural densities of Q_a(x;4,j) (j=0,1,2,3) are considered. We assume a is square-free and a is congruent to 1 (mod 4). Then, for j=0, 2, we can prove unconditionally that their natural densities are equal to 1/3. On the contrary, for j=1, 3, we assume Generalized Riemann Hypothesis, then we can prove that their densities are equal to 1/6. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0211077 | |
| dc.identifier | http://arxiv.org/abs/math/0211077 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65548 | |
| dc.subject | Number Theory | |
| dc.subject | 11N05, 11N25, 11R18 | |
| dc.title | On a distribution property of the residual order of a (mod p) | |
| dc.type | text |