Erdős problem 363

Is it true that there are only finitely many collections of disjoint intervals $I_1,\ldots,I_n$ of size $\lvert I_i\rvert \geq 4$ for $1\leq i\leq n$ such that $\prod_{1\leq i\leq n}\prod_{m\in I_i}m$ is a square?

Sources

The source's own material, retained exactly.

1 retained statement36c6d0fef71a

FormalConjectures/ErdosProblems/

363.lean

Retained formal statement1 of 1

Is it true that there are only finitely many collections of disjoint intervals $I_1,\ldots,I_n$ of size $\lvert I_i\rvert \geq 4$ for $1\leq i\leq n$ such that $\prod_{1\leq i\leq n}\prod_{m\in I_i}m$ is a square?

This is false: Ulas [Ul05] constructed infinitely many such collections.

FormalConjectures/ErdosProblems/363.leanErdos363.erdos_3631 lineExact file

1False ↔ {S | Erdos363.IsValidCollection S}.Finite

SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.