On vanishing sums for roots of unity

1995/11/13 by Lam, T. Y., Leung, K. H. · 10 citations
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.math/9511209

Abstract

Consider the m-th roots of unity in \bf C, where m>0 is an integer. We address the following question: For what values of n can one find n such m-th roots of unity (with repetitions allowed) adding up to zero? We prove that the answer is exactly the set of linear combinations with non-negative integer coefficients of the prime factors of m.

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