For any $M\ge 1$, if $A\subset \mathbb{N}$ is a sufficiently large finite Sidon set then there are at least $M$ many $a\in A+A$ such that $a+1,a-1\notin A+A$.

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

Let (A={a_1<a_2<\dots<a_k}\subset\mathbb N) be a finite **Sidon set** [[nomath]](i.e. all sums $a_i+a_j$ with $i\le j$ are distinct)[[/nomath]]. Put [ S:=A+A={a_i+a_j:\ 1\le i\le j\le k}. ] Then the condition

llm-hunter · gpt pro 5.2 · unverified

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