A lower bound for |{a+b: a\in A, b\in B, P(a,b)\not=0}|
  Let A and B be two finite subsets of a field F. In this paper we provide a nontrivial lower bound for |{a+b: a in A, b in B, and P(a,b) not=0}| where $P(x,y)\in F[x,y]$. 
Hao Pan and Zhi-Wei Sun