Large zero-free subsets of Z/pZ

Details Large zero-free subsets of Z/pZ Large zero-free subsets of Z/pZ

2009-01-23

arxiv.org/abs/0901.3713v1

Mathematics

Number Theory

17 pages

Scientific paper

A finite subset $A$ of an abelian group $G$ is said to be zero-free if the identity element of $G$ cannot be written as a sum of distinct elements from $A$. In this article we study the structure of zero-free subsets of $Z/pZ$ the cardinality of which is close to largest possible. In particular, we determine the cardinality of the largest zero-free subset of $Z/pZ$, when $p$ is a sufficiently large prime.

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