An unsolved problem in number theory asked the following: For a given natural number m, what are the possible integers n for which there exist mth roots of unity We show in this paper that the set of all possible n's is exactly the collection of -combinations of the prime divisors of m, where denot
β¦ LIBER β¦
On Sums of Roots of Unity
β Scribed by Roberto Dvornicich; Umberto Zannier
- Book ID
- 106198894
- Publisher
- Springer Vienna
- Year
- 2000
- Tongue
- English
- Weight
- 118 KB
- Volume
- 129
- Category
- Article
- ISSN
- 0026-9255
No coin nor oath required. For personal study only.
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In an earlier work, the authors determined all possible weights n for which there exists a vanishing sum 1 Ο© ΠΈ ΠΈ ΠΈ Ο© n Ο 0 of mth roots of unity i 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