import Mathlib.Tactic
/-!
# International Mathematical Olympiad 2023, Problem 1
Determine all composite integers n>1 that satisfy the following property:
if d₁,d₂,...,dₖ are all the positive divisors of n with 1=d₁<d₂<...<dₖ=n,
then dᵢ divides dᵢ₊₁ + dᵢ₊₂ for every 1 ≤ i ≤ k-2.
-/
namespace Imo2023P1
/- determine -/ abbrev solution_set : Set ℕ := sorry
abbrev P (n : ℕ) : Prop :=
let divs := n.divisors.sort LE.le
∀ i, (h : i + 2 < divs.length) →
divs.get ⟨i, Nat.lt_of_succ_lt (Nat.lt_of_succ_lt h)⟩ ∣
divs.get ⟨i + 1, Nat.lt_of_succ_lt h⟩ + divs.get ⟨i + 2, h⟩
theorem imo2023_p1 : solution_set = { n | 1 < n ∧ ¬n.Prime ∧ P n } := sorry
end Imo2023P1
This problem does not yet have a complete formalized solution.