An infinite family of multiplicatively independent bases of number systems in cyclotomic number fields

被引：2
|
作者：
Madritsch M.G. [1 ,2 ]
Ziegler V. [3 ]
机构：
[1] Université de Lorraine, Institut Elie Cartan de Lorraine, UMR 7502, Vandoeuvre-lès-Nancy
[2] CNRS, Institut Elie Cartan de Lorraine, UMR 7502, Vandoeuvre-lès-Nancy
[3] Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstr. 69, Linz
来源：
Acta Scientiarum Mathematicarum | 2015年 / 81卷 / 1-2期
关键词：
Canonical number systems; Diophantine equations; Nagell-Ljunggren equation; Radix representations;
D O I：
10.14232/actasm-013-825-5
中图分类号：
学科分类号：
摘要：
Let Χk be a k-th primitive root of unity, m ≥ φ(k)+1 an integer and φk(X) ∈ ℤ[X] the k-th cyclotomic polynomial. In this paper we show that the pair (-m+Χk,N) is a canonical number system, with N = {0, 1, |φk(m)|- 1}. Moreover we also discuss whether the two bases -m+ Χk and -n + Χk are multiplicatively independent for positive integers m, n and k fixed. © Bolyai Institute, University of Szeged.
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页码：33 / 44
页数：11
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