Erdős Problem #1194

Partial progress by GPT-5.4 Pro (23 Apr 2026): partial result. 2 AI contributions are recorded in all.

Problem
Erdős problem #1194 (additive combinatorics, additive basis, sidon sets); current status: open
Credit
GPT-5.4 Pro · AI on its own
Checked
Lean formalizationListed in Tao's wiki
Timeline
First AI contribution 2026-04-23 · wiki data as of 2026-06-30
Sources
Problem page (erdosproblems.com)Tao's AI-contributions wiki
PARTIALPer Tao's AI-contributions wiki

The problem

Let A⊂NA\subset\mathbb{N} be such that every integer n≥1n\geq 1 can be written uniquely as an−bna_n-b_n for some an,bn∈Aa_n,b_n\in A. How fast must an/na_n/n increase?

Statement quoted from erdosproblems.com/1194, maintained by Thomas Bloom. Original source: [Er80,p.100]. Current status there: open.

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Date Kind AI systems Humans Outcome
23 Apr, 2026 AI on its own GPT-5.4 Pro — 🟡 Partial result
2 May, 2026 AI working with humans Codex, GPT-5.5 Pro Lech Mazur 🟡 Partial result (Lean)

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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