The polynomial method and restricted sums of congruence classes

Noga Alon*, Melvyn B. Nathanson, Imre Ruzsa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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
Pages (from-to)404-417
Number of pages14
JournalJournal of Number Theory
Issue number2
StatePublished - Feb 1996


FundersFunder number
Fund for Basic Research
United States Israeli BSF
Center for Discrete Mathematics and Theoretical Computer Science
Rutgers, The State University of New Jersey
Academy of Leisure Sciences
Hungarian Scientific Research Fund1901


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