In additive number theory and combinatorics, a restricted sumset has the form S = { a 1 + ⋯ + a n : a 1 ∈ A 1, …, a n ∈ A n a n d P ≠ 0 }, {\displaystyle S=\{a_{1}+\cdots +a_{n}:\ a_{1}\in A_{1},\ldots,a_{n}\in A_{n}\ \mathrm {and} \ P\not =0\},} where A 1, …, A n {\displaystyle A_{1},\ldots,A_{n}} are finite nonempty subsets of a field F and P {\displaystyle P} is a polynomial over F. If P {\displaystyle P} is a constant non-zero function, for example P = 1 {\displaystyle P=1} for any x 1, …, x n {\displaystyle x_{1},\ldots,x_{n}}, then S {\displaystyle S} is the usual sumset A 1 + ⋯ + A n {\displaystyle A_{1}+\cdots +A_{n}} which is denoted by n A {\displaystyle nA} if A 1 = ⋯ = A n = A. Wikipedia