# The additive basis conjecture

**Conjecture**For every prime , there is a constant (possibly ) so that the union (as multisets) of any bases of the vector space contains an additive basis.

**Definition:** Let be a finite dimensional vector space over the field . We call a multiset with elements in an *additive basis* if for every , there is a subset of which sums to .

It is worth noting that this conjecture would also imply that every -edge-connected graph has a nowhere-zero 3-flow, thus resolving The weak 3-flow conjecture.