On the additive completion of polynomial sets of integers

Ran Donagi*, Marcel Herzog

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let f(x) = Σt=0n ctxt be a polynomial of degree n with nonnegative integral coefficients, and let U: a1 < a2 < ... < ak be the set of integers of the form ai = f(i) that belong to the interval [1, N]. Let B: b1 < b2 < ... < bl be an additive completion of U for the interval [1, N]. Then given ε{lunate} > 0, we have kl > (1 + (n - 1) 2n2 - ε{lunate}) N for sufficiently large N. A similar result is also proved under more general conditions, which suffice for the verification of Hanani's conjecture.

Original languageEnglish
Pages (from-to)150-154
Number of pages5
JournalJournal of Number Theory
Issue number2
StatePublished - May 1971


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