On the Erdos-Turán conjecture

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

doi:10.1016/S0022-314X(03)00108-2

On the Erdos-Turán conjecture

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

Penn State Brandywine

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

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 language	English (US)
Pages (from-to)	339-352
Number of pages	14
Journal	Journal of Number Theory
Volume	102
Issue number	2
DOIs	https://doi.org/10.1016/S0022-314X(03)00108-2
State	Published - Oct 1 2003

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/S0022-314X(03)00108-2

Cite this

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On the Erdos-Turán conjecture

Abstract

All Science Journal Classification (ASJC) codes

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