Improvement of an estimate of H. Mueller involving the order of 2(mod u) II
| dc.creator | Moree, Pieter | |
| dc.date | 2005-07-28 | |
| dc.date | 2005-08-23 | |
| dc.date.accessioned | 2026-07-07T07:38:32Z | |
| dc.date.available | 2026-07-07T07:38:32Z | |
| dc.description | Let m>=1 be an arbitrary fixed integer and let N_m(x) count the number of odd integers u<=x such that the order of 2 modulo u is not divisible by m. In case m is prime estimates for N_m(x) were given by H. Mueller that were subsequently sharpened into an asymptotic estimate by the present author. Mueller on his turn extended the author's result to the case where m is a prime power and gave bounds in the case m is not a prime power. Here an asymptotic for N_m(x) is derived that is valid for all integers m. This asymptotic would easily have followed from Mueller's approach were it not for the fact that a certain Diophantine equation has non-trivial solutions. All solutions of this equation are determined. We also generalize to other base numbers than 2. For a very sparse set of these numbers Mueller's approach does work. | |
| dc.description | 11 pages, 2 Tables; Proposition 3 has now been corrected along with a few typos | |
| dc.identifier | https://arxiv.org/abs/math/0507596 | |
| dc.identifier | http://arxiv.org/abs/math/0507596 | |
| dc.identifier | Arch. Math. 87 (2006), 129-140 | |
| dc.identifier | doi:10.1007/s00013-006-1704-z | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121122 | |
| dc.subject | Number Theory | |
| dc.subject | 11N25, 11A25 | |
| dc.title | Improvement of an estimate of H. Mueller involving the order of 2(mod u) II | |
| dc.type | text |