Solving Erdős Problem 123 with Lean 4 Formal Verification

Solving 20 Erdős Problems with 20 Codex Accounts Running in Parallel

We solved Erdős Problem 123 by proving that every large integer is a sum of distinct terms from pairwise-coprime bases, ensuring no term divides another. Our breakthrough involved a novel 'optional interior shell' construction to overcome previous induction limits. The entire proof is rigorously formalized in Lean 4 using Mathlib, confirming the result without any placeholders.

"The important lesson was that large additive width is not enough; the lower endpoint has to remain under quantitative control."