Let $1 \leq d_{1} < d_{2}$ and $k \geq 3$ . Does there exist an integer $r$ such that if $B = {b_{1} < \dots}$ is a lacunary sequence of positive integers with $b_{i + 1} \geq r b_{i}$ then there exists a sequence of positive integers $A = {a_{1} < \dots}$ such that $d_{1} \leq a_{i + 1} - a_{i} \leq d_{2}$ for all $i \geq 1$ and $(k A) \cap B = \emptyset$ , where $k A$ is the $k$ -fold sumset?

Worked, still open.

additive combinatorics · open · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

unverified AI candidates (2)

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

This is **not known in general** (and in fact it is **false for some parameters**).

llm-hunter · gpt pro 5.2 · unverified

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

open