Let $f (m)$ be such that if $A \subseteq {1, \dots, N}$ has $∣ A ∣ = m$ then every interval in $[1, \infty)$ of length $2 N$ contains $\geq f (m)$ many distinct integers $b_{1}, \dots, b_{r}$ where each $b_{i}$ is divisible by some $a_{i} \in A$ , where $a_{1}, \dots, a_{r}$ are distinct.Estimate $f (m)$ . In particular is it true that $f (m) \leq m$ ?

Worked, still open.

number theory · solved · 0 attempts

use this record

vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Let me restate the problem in matching language, because that makes the combinatorics transparent.

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

solved