putnam-v1 / putnam-1968-a6

putnam-1968-a6

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal putnam-1968-a6

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-1968-a6.lean

import Mathlib

open Finset Polynomial
abbrev putnam_1968_a6_solution : Set ℂ[X] := {X - 1, -(X - 1), X + 1, -(X + 1), X^2 + X - 1, -(X^2 + X - 1), X^2 - X - 1, -(X^2 - X - 1), X^3 + X^2 - X - 1, -(X^3 + X^2 - X - 1), X^3 - X^2 - X + 1, -(X^3 - X^2 - X + 1)}

theorem putnam_1968_a6 : {P : ℂ[X] | P.natDegree ≥ 1 ∧ (∀ k ∈ Set.Icc 0 P.natDegree, P.coeff k = 1 ∨ P.coeff k = -1) ∧
∀ z : ℂ, P.eval z = 0 → ∃ r : ℝ, r = z} = putnam_1968_a6_solution := by
  sorry

Runs (0)

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