The Polynomial Method and Restricted Sums of Congruence Classes Original Research Article

We present a simple and general algebraic technique for obtaining results in Additive Number Theory, and apply it to derive various new extensions of the Cauchy–Davenport Theorem. In particular we obtain, for subsetsA0, A1, …, Akof the finite fieldZp, a tight lower bound on the minimum possible cardinality of[formula]as a function of the cardinalities of the setsAi.