Erdős problem 12 · problems.science

Let $A \subset \mathbb{N}$ be infinite with no distinct $a, b, c \in A$ such that $a \mid (b + c)$ with $b, c > a$ . Can $|A \cap [1, N]|/\sqrt{N}$ have positive lower limit? Must every such $A$ fall below $N^{1-c}$ infinitely often?

Sources

Browse retained paths and inspect the exact material available for this Problem.

10 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

12.lean

Retained formal statement6 of 9

Erdős and Sárközy proved that such an $A$ must have density 0. [ErSa70] Erdős, P. and Sárközi, A., On the divisibility properties of sequences of integers. Proc. London Math. Soc. (3) (1970), 97-101

FormalConjectures/ErdosProblems/12.leanErdos12.erdos_12.variants.erdos_sarkozy_density_01 lineExact file

1∀ (A : Set ℕ), Erdos12.IsGood A → A.HasDensity 0

SolvedStatement only, no proof

Sources

Search problems.science