Find the smallest $h (d)$ such that the following holds. There exists a function $f : N \to {- 1, 1}$ such that, for every $d \geq 1$ , $P_{d} max n \in P_{d} \sum f (n) \leq h (d),$ where $P_{d}$ ranges over all finite arithmetic progressions with common difference $d$ .

Worked, still open.

discrepancy · open · 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

[ D_f(d):=\max_{P_d}\left|\sum_{n\in P_d} f(n)\right| ]

llm-hunter · gpt pro 5.2 · unverified

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

open