The Erdős-Ginzburg-Ziv theorem states that every sequence of 
integers contains 
terms whose sum is divisible by 
. Equivalently, every sequence
of 
elements of the cyclic group 
has an 
-term zero-sum subsequence
(Qu 2026).
The length is sharp. A sequence consisting of 
zeros and 
ones has no 
-term zero-sum subsequence.
Thus the Gao constant of a cyclic
group of order 
is 
.
A counting refinement is the Bialostocki-Lotspeich conjecture, proved by Wang and Zeng (2026).
For higher-rank finite Abelian groups, the corresponding threshold is the Erdős-Ginzburg-Ziv constant.
