Erdős Problem #43

Erdős problem #43 · erdosproblems.com/43

If Sidon sets $A, B \subseteq \{1, \dots, N\}$ satisfy $(A-A) \cap (B-B) = \{0\}$, must $\binom{|A|}{2} + \binom{|B|}{2} \le \binom{f(N)}{2} + O(1)$, where $f(N)$ is the largest Sidon-set size in $[N]$ - and can the bound be improved by a fixed proportion when $|A| = |B|$?

Result

Disproved(see note)

Status

Resolved

AI contribution

AI-discovered

Method

Construction

Field

Number Theory, Sidon Sets

Posed by

—

Year posed

1982

Years open

44y

Solved

2026-04-27

Model

GPT-5.5 Pro, Aristotle, Claude

Vendor

OpenAI / Harmonic / Anthropic

Collaborators

—

Verification

Site-confirmed

Publication

Announced

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article