On consecutive happy numbers
| dc.creator | Pan, Hao | |
| dc.date | 2006-07-08 | |
| dc.date | 2006-07-27 | |
| dc.date.accessioned | 2026-07-07T07:18:11Z | |
| dc.date.available | 2026-07-07T07:18:11Z | |
| dc.description | Let e>=1 and b>=2 be integers. For a positive integer n=\sum_{j=0}^ka_jb^j with 0<=a_j<b, define T_{e,b}(n)=\sum_{j=0}^ka_j^e. n is called (e,b)-happy if T_{e,b}^r(n)=1 for some r>=0, where T_{e,b}^r is the r-th iteration of T_{e,b}. In this paper, we prove that there exist arbitrarily long sequences of consecutive (e,b)-happy numbers provided that e-1 is not divisible by p-1 for any prime divisor p of b-1. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0607213 | |
| dc.identifier | http://arxiv.org/abs/math/0607213 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114207 | |
| dc.subject | Number Theory | |
| dc.subject | Primary 11A63; Secondary 11A07, 11B05 | |
| dc.title | On consecutive happy numbers | |
| dc.type | text |