The four roots lemma

Kristijan Tabak
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 20, 2014, Number 5, Pages 14–19
Full paper (PDF, 172 Kb)

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Authors and affiliations

Kristijan Tabak
Rochester Institute of Technology, Zagreb Campus
D. T. Gavrana 15, 10000 Zagreb, Croatia

Abstract

Using pairwise abbreviation and simple characterization of zero-sums over ℤ[ε]; where ε is root of unity of order 2ⁿ, we manage to prove that a norm of a sum of any four mutually different roots has to be different that 2.

Keywords

• Norm invariance.
• Group ring.
• Pairwise abbreviation.

AMS Classification

• 11S05
• 11T06

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