The Number of k-Sums Modulo k
Let a1, ..., ar be a sequence of elements of Zk, the integers modulo k. Calling the sum of k terms of the sequence a k-sum, how small can the set of k-sums be? Our aim in this paper is to show that if 0 is not a k-sum then there are at least r-k+1 k-sums. This result, which is best possible, extends the Erdos-Ginzburg-Ziv theorem, which states that if r=2k-1 then 0 is a k-sum. We also show that the same result holds in any abelian group of order k, and make some related conjectures. © 1999 Academic Press.
Journal of Number Theory
Bollobás, B., & Leader, I. (1999). The Number of k-Sums Modulo k. Journal of Number Theory, 78 (1), 27-35. https://doi.org/10.1006/jnth.1999.2405