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Erdős problem 363

Is it true that there are only finitely many collections of disjoint intervals I1,…,InI_1,\ldots,I_n of size ∣Ii∣≥4\lvert I_i\rvert \geq 4 for 1≤i≤n1\leq i\leq n such that∏1≤i≤n∏m∈Iim\prod_{1\leq i\leq n}\prod_{m\in I_i}mis a square?

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1 retained statement2415f78e850a

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FormalConjectures/ErdosProblems/

363.lean

Retained formal statement1 of 1

Is it true that there are only finitely many collections of disjoint intervals I1,…,InI_1,\ldots,I_n of size ∣Ii∣≥4\lvert I_i\rvert \geq 4 for 1≤i≤n1\leq i\leq n such that∏1≤i≤n∏m∈Iim\prod_{1\leq i\leq n}\prod_{m\in I_i}mis a square?

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

FormalConjectures/ErdosProblems/363.leanErdos363.erdos_3631 lineExact file
False ↔ {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.

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