On the Erdos-Turán conjecture

G. Grekos, Labib Haddad, C. Helou, Jukka Pihko

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Abstract

We give equivalent formulations of the Erdos-Turán conjecture on the unboundedness of the number of representations of the natural numbers by additive bases of order two of ℕ. These formulations allow for a quantitative exploration of the conjecture. They are expressed through some functions of x ∈ ℕ reflecting the behavior of bases up to x. We examine some properties of these functions and give numerical results showing that the maximum number of representations by any basis is ≥6.

Original languageEnglish (US)
Pages (from-to)339-352
Number of pages14
JournalJournal of Number Theory
Volume102
Issue number2
DOIs
StatePublished - Oct 1 2003

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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