Simple arguments on consecutive power residues
| dc.creator | Sun, Zhi-Wei | |
| dc.date | 2003-11-29 | |
| dc.date | 2007-02-22 | |
| dc.date.accessioned | 2026-07-07T07:47:58Z | |
| dc.date.available | 2026-07-07T07:47:58Z | |
| dc.description | By some extremely simple arguments, we point out the following: (i) If n is the least positive k-th power non-residue modulo a positive integer m, then the greatest number of consecutive k-th power residues mod m is smaller than m/n. (ii) Let O_K be the ring of algebraic integers in a quadratic field $K=Q(\sqrt d)$ with d in {-1,-2,-3,-7,-11}. Then, for any irreducible $π\in O_K$ and positive integer k not relatively prime to $π\barπ-1$, there exists a k-th power non-residue $ω\in O_K$ modulo $π$ such that $|ω|<\sqrt{|π|}+0.65$. | |
| dc.description | 5 pages | |
| dc.identifier | https://arxiv.org/abs/math/0312010 | |
| dc.identifier | http://arxiv.org/abs/math/0312010 | |
| dc.identifier | J. Number Theory 124(2007), no.1, 57--61 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124346 | |
| dc.subject | Number Theory | |
| dc.subject | 11A15; 05A19; 11A07; 11R11 | |
| dc.title | Simple arguments on consecutive power residues | |
| dc.type | text |