ON VANISHING SUMS FOR ROOTS OF UNITY

Tsit-Yuen Lam and K. H. Leung

Abstract. Consider the m-th roots of unity in 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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