On Kemnitz’ conjecture concerning lattice-points in the plane Authors Article

Received: 25 May 2004 Accepted: 14 February 2005 DOI :
10.1007/s11139-006-0256-y

Cite this article as: Reiher, C. Ramanujan J (2007) 13: 333. doi:10.1007/s11139-006-0256-y
Abstract In 1961, Erdős, Ginzburg and Ziv proved a remarkable theorem stating that each set of 2n −1 integers contains a subset of size n , the sum of whose elements is divisible by n . We will prove a similar result for pairs of integers, i.e. planar lattice-points, usually referred to as Kemnitz’ conjecture.

Keywords Zero-sum-subsets Kemnitz’ Conjecture Dedicated to Richard Askey on the occasion of his 70th birthday.

2000 Mathematics Subject Classification Primary—11B50.

References 1.

Alon, N., Dubiner, D.: A lattice point problem and additive number theory. Combinatorica

15 , 301–309 (1995)

CrossRef MathSciNet 2.

Erdős, P., Ginzburg, A., Ziv, A.: Theorem in the additive number theory. Bull Research Council Israel 10F , 41–43 (1961)

3.

Gao, W.: Note on a zero-sum problem. J. Combin. Theory, Series A

95 , 387–389 (2001)

CrossRef 4.

Kemnitz, A.: On a lattice point problem. Ars Combin.

16b , 151–160 (1983)

MathSciNet 5.

Rónyai, L.: On a conjecture of Kemnitz. Combinatorica

20 , 569–573 (2000)

CrossRef MathSciNet 6.

Schmidt, W.M.: Equations Over Finite Fields, An Elementary Approach. Springer Verlag, Lecture Notes in Math (1976)

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