# co.combinatorics – Visiting zero-sum triples in a vector space Answer

Hello dear visitor to our network We will offer you a solution to this question co.combinatorics – Visiting zero-sum triples in a vector space ,and the answer will be typical through documented information sources, We welcome you and offer you new questions and answers, Many visitor are wondering about the answer to this question.

## co.combinatorics – Visiting zero-sum triples in a vector space

Is it true that for any set $$A\subset\mathbb F_5^n$$ satisfying $$A\cap(-A)=\varnothing$$there is a subset $$A’\subseteq A$$ search any triple $$(a,b,c)\in A\times A\times A$$ with $$a+b+c=0$$ has exactly one or two of its components lying in $$A’$$? That is, no zero-sum triple has all of its components in $$A’$$and no zero-sum triple is completely avoided by $$A’$$.

The same question can be asked for any abelian group, but (the additive group of) $$\mathbb F_5^n$$ is what I presently need. I do not know how relevant the assumption $$A\cap(-A)=\varnothing$$ is.

we will offer you the solution to co.combinatorics – Visiting zero-sum triples in a vector space question via our network which brings all the answers from multiple reliable sources.