Let $f(N)$ be the size of the largest quasi-Sidon subset $A\subset \{1,\dots ,N\}$, where we say that $A$ is quasi-Sidon if$$|A+A|=(1+o(1))\left(\genfrac{}{}{0ex}{}{|A|}{2}\right).$$How does $f(N)$ grow?

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

A quasi‑Sidon set (A\subset{1,\dots,N}) has “almost all” pairwise sums distinct, in the sense that [ |A+A|=(1+o(1))\binom{|A|}{2}\sim \frac{|A|^2}{2}. ]

llm-hunter · gpt pro 5.2 · unverified

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