Problems/Erdos Problem #457

Erdos Problem #457

Number TheorySOLVED

Year

1980

Difficulty

*****

Solved by

Aristotle + GPT-5.2 Pro (2026)

Statement

A number-theoretic problem resolved autonomously by AI with formal verification.

\text{Full AI solution (Lean), Mar 2026}

About this Problem

Fully resolved autonomously by AI. Part of the growing wave of Erdos problems falling to AI theorem provers.

AI Contributions

Full SolutionLeanMar 2, 2026

Full solution with Lean proof.

Tools: Aristotle, GPT-5.2 Pro

About the Lean 4 Prover

Lean 4 is a theorem prover and programming language. When a proof compiles in Lean, it is mathematically certain to be correct — the type checker verifies every logical step. This is the gold standard for formal verification.

Our platform uses fal.ai serverless compute to run Lean verification, and Gemini to generate proof strategies that are then formally checked. ShinkaEvolve provides the evolutionary backbone for automated mathematical discovery.

Mathematical Art

Generate a unique AI illustration of this problem using fal.ai FLUX.

Connected Constellations