Let $k \geq 3$ and $g_{k} (N)$ be minimal such that if $A \subseteq {1, \dots, 2 N}$ has $∣ A ∣ \geq N + g_{k} (N)$ then there exist integers $b_{1}, \dots, b_{k}$ such that all $(2 k)$ pairwise sums are in $A$ (but the $b_{i}$ themselves need not be in $A$ ).Estimate $g_{k} (N)$ .

Worked, still open.

number theory · open · possible · 0 attempts

use this record

vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

unverified AI candidates (2)

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

As stated [[nomath]](allowing the $b_i$ to repeat)[[/nomath]], the threshold is completely controlled by **parity**, and one gets an exact answer:

llm-hunter · gpt pro 5.2 · unverified

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

shown · paper

open