Skolem conjectured that the "power sum" A(n) = λ₁α₁ⁿ + ⋯ + λₘαₘⁿ satisfies a certain local-global principle. We prove this conjecture in the case when the multiplicative group generated by α₁,...,αₘ is of rank 1.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa159-2-1,
author = {Boris Bartolome and Yuri Bilu and Florian Luca},
title = {On the exponential local-global principle},
journal = {Acta Arithmetica},
volume = {161},
year = {2013},
pages = {101-111},
zbl = {1330.11019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa159-2-1}
}
Boris Bartolome; Yuri Bilu; Florian Luca. On the exponential local-global principle. Acta Arithmetica, Tome 161 (2013) pp. 101-111. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa159-2-1/