The Erdős–Turán conjecture is an old unsolved problem in additive number theory (not to be confused with Erdős conjecture on arithmetic progressions) posed by Paul Erdős and Pál …

Erdős' conjecture on arithmetic progressions, often referred to as the Erdős–Turán conjecture, is a conjecture in arithmetic combinatorics (not to be confused with the Erdős–Turán conjecture …

2003年10月1日 · We give equivalent formulations of the Erdős–Turán conjecture on the unboundedness of the number of representations of the natural numbers by additive bases of …

Erdős offered a $3000 prize for a proof of the proposition that "If the sum of reciprocals of a set of integers diverges, then that set contains arbitrarily long arithmetic progressions." This …

2020年8月18日 · The Erdos-Turan conjecture in additive combinatorics is one of the longest lasting unsolved problems. The two mathematicians used density to prove that a certain set …

Erdos-Turan Conjecture for order two bases: If $ B $ is an additive basis of order 2, then $ r_B $ is unbounded. Are there any serious strategies for attacking this conjecture? If so, what are they?

Two positive results are a theorem of Dirac [D] which shows that cannot be constant from some point on, and a theorem of Borwein, Choi, and Chu [BCC] which shows that cannot be …

The Erdos and Turan· [1] conjecture states: Conjecture 1 For any basis set B, r(B;n) is unbounded. Equivalently, for any set B ‰N, r(B;n) > 0;8n 2N ¡!limsup n!1 r(B;n) = 1 (1) The …

2021年5月1日 · In this paper, we make progress on the conjecture of Erdős and Simonovits. First, we show that 2 − a b is realisable for any integers a, b ≥ 1 with b> a and b ≡ ± 1 (mod a). This …

2015年5月1日 · In particular, we call A ⊆ N a basis of order k if r k (A, n) ≥ 1 for all n ≥ 0. The well-known Erdős–Turán conjecture [4] states that if A is an asymptotic basis of order 2, then r 2 …