Sums of roots of unity vanishing modulo a prime

On Vanishing Sums of Roots of Unity

✍ T.Y Lam; K.H Leung 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 150 KB

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

Vanishing Sums ofmth Roots of Unity in F

Vanishing Sums ofmth Roots of Unity in Finite Fields

✍ T.Y. Lam; K.H. Leung 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 273 KB

In an earlier work, the authors determined all possible weights n for which there exists a vanishing sum 1 ϩ и и и ϩ n ϭ 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

Enumeration of power sums modulo a prime

✍ Andrew M. Odlyzko; Richard P. Stanley 📂 Article 📅 1978 🏛 Elsevier Science 🌐 English ⚖ 418 KB

Sums of subsequences modulo prime powers

✍ N. Alon 📂 Article 📅 1988 🏛 Elsevier Science 🌐 English ⚖ 130 KB

Roots of Polynomials Modulo Prime Powers

✍ Bruce Dearden; Jerry Metzger 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 202 KB

In general , not every set of values modulo n will be the set of roots modulo n of some polynomial . In this note , some characteristics of those sets which are root sets modulo a prime power are developed , and these characteristics are used to determine the number of dif ferent sets of integers wh

Galois ε-factors modulo roots of unity

✍ Guy Henniart 📂 Article 📅 1984 🏛 Springer-Verlag 🌐 English ⚖ 473 KB