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?

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10 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

12.lean

Retained formal statement3 of 9

Let $A$ be an infinite set such that there are no distinct $a,b,c \in A$ such that $a \mid (b+c)$ and $b,c > a$ . Is it true that $∑_{n \in A} \frac{1}{n} < \infty$ ?

FormalConjectures/ErdosProblems/12.leanErdos12.erdos_12.parts.iii1 lineExact file

1sorry ↔ ∀ (A : Set ℕ), Erdos12.IsGood A → Summable fun n => 1 / ↑↑n

OpenStatement only, no proof

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