The polynomial method and restricted sums of congruence classes

Noga Alon, Melvyn B. Nathanson, Imre Ruzsa

Research output: Contribution to journalArticlepeer-review

93 Scopus citations


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 subsets A0, A1, ..., Ak of the finite field Zp, a tight lower bound on the minimum possible cardinality of {a0 + a1 + ⋯ + ak: ai∈ Ai, ai ≠ aj for 0 ≤ i < j ≤ k} as a function of the cardinalities of the sets Ai.

Original languageEnglish (US)
Pages (from-to)404-417
Number of pages14
JournalJournal of Number Theory
Issue number2
StatePublished - Feb 1996
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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