Let $A$ be a set of $n$ integers. How many distinct $d$ can occur as the common difference of a three-term arithmetic progression in $A$?In particular, are there always $O(n^{3/2})$ many such $d$?

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

Let [ D(A):={,d\in \mathbb Z\setminus{0}:\ \exists a\in\mathbb Z\ \text{with}\ a,\ a+d,\ a+2d\in A,} ] [[nomath]](the set of *distinct* nonzero common differences of 3-term arithmetic progressions in $A$)[[/nomath]]. Counting (d>0) or (d\neq 0) only changes things by a factor of $2$.

llm-hunter · gpt pro 5.2 · unverified

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