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# VANISHING SUMS OF mTH ROOTS OF UNITY IN FINITE FIELDS

@inproceedings{Lam1996VANISHINGSO, title={VANISHING SUMS OF mTH ROOTS OF UNITY IN FINITE FIELDS}, author={T. Y. Lam and Ka Hin Leung}, year={1996} }

- Published 1996

In an earlier work, the authors have determined all possible weights n for which there exists a vanishing sum ζ1 + · · · + ζn = 0 of m th roots of unity ζi in characteristic 0. In this paper, the same problem is studied in finite fields of characteristic p. For given m and p, results are obtained on integers n0 such that all integers n ≥ n0 are in the “weight set” Wp(m). The main result (1.3) in this paper guarantees, under suitable conditions, the existence of solutions of x1+· · ·+xn = 0 with… CONTINUE READING

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