A generalization of the Erdos-Suranyi problem

作者：Miyanohara Eiji^*

来源：Indagationes Mathematicae, 2017, 28(2): 353-361.

DOI：10.1016/j.indag.2016.08.002

• Theorem of Erdos and Suranyi
• The set of roots of unity
• Prielipp's problem
• Representation of integers
• Signed sums

Erdos-Suranyi and Prielipp suggested to study the following problem: For any integers k > 0 and n, are there an integer N and a map is an element of : {1, N} -> {-1, 1} such that
n = Sigma(N)(j=1) is an element of(j) j(k) ? (0.1)
Mitek and Bleicher independently solved this problem affirmatively.
In this paper we consider the case that for some positive odd integer L the numbers is an element of(j) are L-th roots of unity. We show that the answer to the corresponding question is negative if and only if L is a prime power.

• 出版日期2017-4