# On the Uniform Distribution in Residue Classes of Dense Sets of Integers with Distinct Sums

@article{Kolountzakis1998OnTU, title={On the Uniform Distribution in Residue Classes of Dense Sets of Integers with Distinct Sums}, author={Mihail N. Kolountzakis}, journal={Journal of Number Theory}, year={1998}, volume={76}, pages={147-153} }

Abstract A set A ⊆{1, …, N } is of the type B 2 if all sums a + b , with a ⩾ b , a , b ∈ A , are distinct. It is well known that the largest such set is of size asymptotic to N 1/2 . For a B 2 set A of this size we show that, under mild assumptions on the size of the modulus m and on the difference N 1/2 −| A | (these quantities should not be too large), the elements of A are uniformly distributed in the residue classes mod m . Quantitative estimates on how uniform the distribution is are…

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