Claims

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1968_07_01_olson: Olson (J. Combinatorial Theory, 1968) proves that more than (4p - 3)^{1/2} distinct nonzero residues modulo a prime p have a nonempty zero-sum subfamily, the prime case with the constant 2; refereed, credited by the site.

1969_05_15_szemeredi: Szemerédi's theorem (Acta Arith., 1970) that in every abelian group of order n, any c times the square root of n elements have a nonempty zero-sum subset; refereed, acknowledged by Erdős and accepted by the site.

1996_01_18_hamidoune_zemor: Hamidoune and Zémor (Acta Arith., 1996) prove that more than sqrt(2n) + O(n^{1/3} ln n) elements of an abelian group of order n have a nonempty zero-sum subset; refereed, credited by the site.

2009_07_20_balandraud: Balandraud (Israel J. Math., 2012) proves Selfridge's conjecture: a largest zero-sum free subset of Z/pZ has k elements, k the greatest integer with k(k+1)/2 < p; refereed, credited by the site.

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