Problems/Erdos-Turan Conjecture on Additive Bases

Erdos-Turan Conjecture on Additive Bases

Number TheoryOPEN
Year
1941
Difficulty
*****

Statement

If B is an additive basis of order 2, the representation function is unbounded.

lim sup⁡n→∞rB,2(n)=∞\limsup_{n\to\infty} r_{B,2}(n) = \infty

About this Problem

Asserts no 'thin' additive basis exists. Central to additive number theory for over 80 years.

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