Erdős Problem 866

### What is the conjecture

https://www.erdosproblems.com/866

Let $k\geq 3$ and $g_k(N)$ be minimal such that if $A\subseteq \\{1,\ldots,2N\\}$ has $\lvert A\rvert \geq N+g_k(N)$ then there exist integers $b_1,\ldots,b_k$ such that all $\binom{k}{2}$ pairwise sums are in $A$ (but the $b_i$ themselves need not be in $A$).

Estimate $g_k(N)$.

Status: open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else