## Compfiles: Catalog Of Math Problems Formalized In Lean

## Imo1985P4

```
import Mathlib.Tactic
/-!
# International Mathematical Olympiad 1985, Problem 4
Given a set M of 1985 distinct positive integers, none of which has a prime
divisor greater than 23, prove that M contains a subset of 4 elements
whose product is the 4th power of an integer.
-/
namespace Imo1985P4
theorem imo1985_p4 (M : Finset ℕ) (Mpos : ∀ m ∈ M, 0 < m)
(Mdivisors : ∀ m ∈ M, ∀ n, m.Prime ∧ n ∣ m → m ≤ 23)
: ∃ M' : Finset ℕ, M' ⊆ M ∧ ∃ k, M'.prod id = k^4 := sorry
end Imo1985P4
```

This problem does not yet have a complete formalized solution.

Open with the in-brower editor at live.lean-lang.org: