putnam-v1 / putnam-1963-a4

putnam-1963-a4

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal putnam-1963-a4

What it runs

The Lean statement the swarm must prove — kernel-verified at Gate A. The trailing sorry is the open obligation a proof replaces.

goals/putnam-1963-a4.lean

import Mathlib

open Filter Set

theorem putnam_1963_a4 (T : (ℕ → ℝ) → (ℕ → ℝ))
    (T_def : ∀ a n, T a n = n * ((1 + a (n + 1)) / a n - 1))
    (P : (ℕ → ℝ) → ℝ → Prop)
    (P_def : ∀ a C, P a C ↔ C ≤ limsup (T a) atTop ∨ ¬ BddAbove (range (T a))) :
    (∀ a, (∀ n, 0 < a n) → P a 1) ∧ (∀ C > 1, ∃ a, (∀ n, 0 < a n) ∧ ¬ P a C) := by
  sorry

Runs (0)

No runs recorded for this suite yet — they appear here as the swarm attempts the benchmarks.