putnam-v1 / putnam-1963-b3

putnam-1963-b3

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal putnam-1963-b3

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-b3.lean

import Mathlib

open Topology Filter Polynomial
abbrev putnam_1963_b3_solution : Set (ℝ → ℝ) := {(fun u : ℝ => A * Real.sinh (k * u)) | (A : ℝ) (k : ℝ)} ∪ {(fun u : ℝ => A * u) | A : ℝ} ∪ {(fun u : ℝ => A * Real.sin (k * u)) | (A : ℝ) (k : ℝ)}

theorem putnam_1963_b3 (f : ℝ → ℝ) :
    f ∈ putnam_1963_b3_solution ↔
      (ContDiff ℝ 1 f ∧ Differentiable ℝ (deriv f) ∧
      ∀ x y : ℝ, (f x) ^ 2 - (f y) ^ 2 = f (x + y) * f (x - y)) := by
  sorry

Runs (0)

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