Lam–Leung: vanishing sums of roots of unity

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Library card.

T. Y. Lam and K. H. Leung, "On vanishing sums of roots of unity," Journal of Algebra 224 (2000), no. 1, 91--109.

Lam and Leung determine the possible weights of vanishing sums of $n$-th roots of unity with nonnegative integer coefficients: the weight lies in the additive semigroup generated by the prime divisors of $n$. They also show that when $n$ has at most two distinct prime divisors every minimal vanishing sum is, up to rotation, a prime cycle.