Compfiles: Catalog Of Math Problems Formalized In Lean

Imo1995P4

import Mathlib.Tactic

/-!
# International Mathematical Olympiad 1995, Problem 4

The positive real numbers $x_0, x_1, x_2,.....x_{1994}, x_{1995}$ satisfy the relations
$x_0=x_{1995}$ and $x_{i-1}+\frac{2}{x_{i-1}}=2{x_i}+\frac{1}{x_i}$
for $i=1,2,3,....1995$
Find the maximum value that $x_0$ can have.
-/

namespace Imo1995P4

/- determine -/ abbrev solution : ℝ := sorry

theorem imo1995_p4
  (x : ℕ → ℝ)
  (h : x 0 = x 1995)
  (h1 : ∀ i : ℕ, 0 < i ∧ i ≤ 1995 → x (i - 1) + (2 / x (i - 1)) = 2 * x i + (1 / x i)) :
  x 0 ≤ solution ∧
  (∃ x : ℕ → ℝ, x 0 = solution ∧
    x 0 = x 1995 ∧
    ∀ i : ℕ, 0 < i ∧ i ≤ 1995 → x (i - 1) + (2 / x (i - 1)) = 2 * x i + (1 / x i)) := sorry


end Imo1995P4

File author(s): InternLM-MATH LEAN Formalizer v0.1

This problem does not yet have a complete formalized solution.