The four roots lemma

Kristijan Tabak
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 20, 2014, Number 5, Pages 14—19
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Authors and affiliations

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


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.


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

AMS Classification

  • 11S05
  • 11T06


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Cite this paper

Tabak, K. (2014). The four roots lemma. Notes on Number Theory and Discrete Mathematics, 20(5), 14-19.

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