Erdős problem 1145 · problems.science

Let $A=\{1\leq a_1 < a_2 < \cdots\}$ and $B=\{1\leq b_1 < b_2 < \cdots\}$ be sets of integers with $a_n/b_n\to 1$ .

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2 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

1145.lean

Retained formal statement1 of 2

Let $A=\{1\leq a_1 < a_2 < \cdots\}$ and $B=\{1\leq b_1 < b_2 < \cdots\}$ be sets of integers with $a_n/b_n\to 1$ .

If $A+B$ contains all sufficiently large positive integers then is it true that $\limsup 1_A\ast 1_B(n)=\infty$ ?

A conjecture of Erdős and Sárközy.

FormalConjectures/ErdosProblems/1145.leanErdos1145.erdos_11451 lineExact file

1True ↔ Erdos1145.Erdos1145Prop

OpenStatement only, no proof