Asymptotically exact heuristics for prime divisors of a^k+b^k
| dc.creator | Moree, Pieter | |
| dc.date | 2003-11-26 | |
| dc.date.accessioned | 2026-07-07T06:30:52Z | |
| dc.date.available | 2026-07-07T06:30:52Z | |
| dc.description | Let N_{a,b}(x) count the number of primes p<=x with p dividing a^k+b^k for some k>=1. It is known that asymptotically N_{a,b}(x) grows like c(a,b)x/log x for some rational number c(a,b) that depends in a rather intricate way on a and b. A simple heuristic formula for N_{a,b}(x) is proposed and it is proved that it is asymptotically exact, i.e. has the same asymptotic behaviour as N_{a,b}(x). Connections with Ramanujan sums and character sums are discussed. | |
| dc.description | 11 pages, 1 table | |
| dc.identifier | https://arxiv.org/abs/math/0311483 | |
| dc.identifier | http://arxiv.org/abs/math/0311483 | |
| dc.identifier | J. Integer Seq. 9 (2006), Article 06.2.8 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98454 | |
| dc.subject | Number Theory | |
| dc.subject | 11N37; 11B83 | |
| dc.title | Asymptotically exact heuristics for prime divisors of a^k+b^k | |
| dc.type | text |