A remark on Zoloterav's theorem
| dc.creator | Pan, Hao | |
| dc.date | 2006-01-02 | |
| dc.date.accessioned | 2026-07-07T06:58:27Z | |
| dc.date.available | 2026-07-07T06:58:27Z | |
| dc.description | Let n>=3 be an odd integer. For any integer a prime to n, define the permutation gamma_{a,n} of {1,...,(n-1)/2} by gamma_{a,n}(x)=n-\dec{ax}_n if {ax}_n>=(n+1)/2, and {ax}_n if {ax}_n<=(n-1)/2, where {x}_n denotes the least nonnegative residue of x modulo n. In this note, we show that the sign of gamma_{a,n} coincides with the Jacobi symbol (a/n) if n=1 mod 4, and 1 if n=3 mod 4. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0601026 | |
| dc.identifier | http://arxiv.org/abs/math/0601026 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107364 | |
| dc.subject | Number Theory | |
| dc.subject | 11A07; 11A15 | |
| dc.title | A remark on Zoloterav's theorem | |
| dc.type | text |