On the exponential local-global principle
Volume 159 / 2013
Acta Arithmetica 159 (2013), 101-111
MSC: Primary 11D61; Secondary 11J86, 11J87.
DOI: 10.4064/aa159-2-1
Abstract
Skolem conjectured that the “power sum” ${A(n)=\lambda _1 \alpha _1^n + \cdots + \lambda _m \alpha _m^n}$ satisfies a certain local-global principle. We prove this conjecture in the case when the multiplicative group generated by ${\alpha _1, \ldots , \alpha _m}$ is of rank $1$.
