Are there non-trivial triples with a zero sums in a given subset of an n-dimensional vector space modulo 3? The main theorem, which we examine in this project, states that such a triple exists when the subset is big enough,or, more specifically, when its density is more than or equal to 8/n.
In this project we manage to lower the boundary for its size almost two times – it turns out the theorem is true for every subset of density more than 4/n. We also suggest a generalisation of the theorem, where we sum k-tuples modulo k > 3, and find an analogical boundary, dependent on n and k.

Scientific field

Mathematics

Country

Bulgaria

Contestants

Pressiana Ivaylova Marinova