On the possible orders of a basis for a finite cyclic group
Abstract
We prove a conjecture of Dukes and Herke concerning the possible orders of a basis for the cyclic group Zn, namely : For each k ∈ N there exists a constant ck > 0 such that, for all n ∈ N, if A ⊂eq Zn is a basis of order greater than n/k, then the order of A is within ck of n/l for some integer l ∈ [1,k]. The proof makes use of various results in additive number theory concerning the growth of sumsets.
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