Sylvester's Theorem

Balancing Centrifuges: Vanishing Sums of Roots of Unity

Achyut Bharadwaj, Tanmay Gupta, James Shuffelton, Toyesh Jayaswal, Matt Baker
August 2022
Sivek's Theorem, Lam and Leung's Theorem, Sylvester's Theorem, vanishing sums, roots of unity

Abstract # The problem of balancing centrifuges is equivalent to finding sets of $k$ $n$-th roots of unity that sum to $0$. We can represent each slot in the centrifuge as an $n$-th root of unity as the slots in the centrifuge are also equally spaced and equidistant from the origin. Acknowledgements # Accepted for publication at the Joint Mathematics Meetings, Boston, January 4 – 7, 2023. This work was carried out as part of a research project at PROMYS-2022. ...