Compfiles: Catalog Of Math Problems Formalized In Lean

Imo1991P6


import Mathlib.Tactic

/-!
# International Mathematical Olympiad 1991, Problem 6

An infinite sequence x₀,x₁,x₂,... of real numbers is said to be *bounded*
if there is a constant C such that |xᵢ| ≤ C for every i ≥ 0.

Given any real number a > 1, construct a bounded infinite sequence
x₀,x₁,x₂,... such that

                  |xᵢ - xⱼ|⬝|i - j| ≥ 1

for every pair of distinct nonnegative integers i, j.
-/

namespace Imo1991P6

abbrev Bounded (x : ℕ → ℝ) : Prop := ∃ C, ∀ i, |x i| ≤ C

/- determine -/ abbrev solution (a : ℝ) (ha : 1 < a) : ℕ → ℝ := sorry

theorem imo1991_p6 (a : ℝ) (ha : 1 < a) :
    Bounded (solution a ha) ∧
    ∀ i j, i ≠ j →
      1 ≤ |solution a ha i - solution a ha j| * |(i:ℝ) - j| := sorry

This problem does not yet have a complete formalized solution.

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