Let $A\subset \mathbb{R}$ be a set of size $n$ such that every subset $B\subseteq A$ with $|B|=4$ has $|B-B|\ge 11$. Find the best constant $c>0$ such that $A$ must always contain a Sidon set of size $\ge cn$.

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

For a 4–element set (B={b_1<b_2<b_3<b_4}), the difference set $B-B$ consists of $0$ plus all (\pm(b_j-b_i)) with (j>i). There are at most $6$ positive differences, so [ |B-B|=1+2\cdot |{b_j-b_i:\ j>i}|. ] Thus (|B-B|\ge 11) is equivalent to saying that among the $6$ positive pairwise differences, **at least $5$ are dis…

llm-hunter · gpt pro 5.2 · unverified

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