Olson's theorem for cyclic groups

Abstract

Let $n$ be a large number. A subset $A$ of $Z_n$ is complete if $S_A=Z_n$, where $S_A$ is the collection of the subset sums of $A$. Olson proved that if $n$ is a prime and $|A|>2n^{1/2}$, then $S_A$ is complete. We show that a similar result for the case when $n$ is a composite number, using a different approach.

Cited by in corpus (2)

• A quadratic lower bound for subset sums
• Long arithmetic progressions in sumsets: Thresholds and Bounds