In mathematics, the Davenport constant D(G ) is an invariant of a group studied in additive combinatorics, quantifying the size of nonunique factorizations.
Given a finite abelian group G, D(G ) is defined as the smallest number such that every sequence of elements of that length contains a non-empty subsequence adding up to 0.
In symbols, this is[1] The original motivation for studying Davenport's constant was the problem of non-unique factorization in number fields.
This observation implies that Davenport's constant determines by how much the lengths of different factorization of some element in
[5][citation needed] The upper bound mentioned above plays an important role in Ahlford, Granville and Pomerance's proof of the existence of infinitely many Carmichael numbers.