A lower bound for |{a + b: a ∈ A, b ∈ B, P(a,b) ≠ 0}|

Authors:
Hao Pan;Zhi-Wei Sun
Affiliations:
Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China;Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China
Venue:
Journal of Combinatorial Theory Series A
Year:
2002

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Abstract

Let A and B be two finite subsets of a field F. In this paper, we provide a non-trivial lower bound for |{a + b: a ∈ A, b ∈ B, and P(a, b) ≠ 0}| where P(x, y) ∈ F[x, y].