On vanishing sums for roots of unity

Details On vanishing sums for roots of unity On vanishing sums for roots of unity

1995-11-13

arxiv.org/abs/math/9511209v1

Mathematics

Number Theory

Scientific paper

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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