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Miklós Schweitzer 2012 P2

Source: Miklós Schweitzer 2012 P2

August 20, 2018
linear algebra

Problem Statement

Call a subset AA of the cyclic group (Zn,+)(\mathbb{Z}_n,+) rich if for all x,y∈Znx,y \in \mathbb{Z}_n there exists r∈Znr \in \mathbb{Z}_n such that x−r,x+r,y−r,y+rx-r,x+r,y-r,y+r are all in AA. For what α\alpha is there a constant Cα>0C_\alpha>0 such that for each odd positive integer nn, every rich subset A⊂ZnA \subset \mathbb{Z}_n has at least CαnαC_\alpha n^\alpha elements?
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