Congruence ABC implies ABC
| dc.creator | Ellenberg, Jordan S. | |
| dc.date | 1999-09-17 | |
| dc.date.accessioned | 2026-07-07T05:30:48Z | |
| dc.date.available | 2026-07-07T05:30:48Z | |
| dc.description | The ABC conjecture of Masser and Oesterle' states that if (a,b,c) are coprime integers with a + b + c = 0, then sup(|a|,|b|,|c|) < c_e (rad(abc))^{1+e} for any e > 0. Oesterle' has observed that if the ABC conjecture holds for all (a,b,c) with 16 | abc, then the full ABC conjecture holds. We extend that result to show that, for every integer N, the "congruence ABC conjecture" that ABC holds for all (a,b,c) with N|abc implies the full ABC conjecture. | |
| dc.description | 4 pages; to appear, Indag. Math | |
| dc.identifier | https://arxiv.org/abs/math/9909098 | |
| dc.identifier | http://arxiv.org/abs/math/9909098 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79116 | |
| dc.subject | Number Theory | |
| dc.subject | 11D41 (Primary) 11D75 (Secondary) | |
| dc.title | Congruence ABC implies ABC | |
| dc.type | text |