minif2f-v1 / amc12a-2002-p12

amc12a-2002-p12

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal amc12a-2002-p12

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/amc12a-2002-p12.lean

import Mathlib

set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat

theorem amc12a_2002_p12 (f : ℝ → ℝ) (k : ℝ) (a b : ℕ) (h₀ : ∀ x, f x = x ^ 2 - 63 * x + k)
  (h₁ : f a = 0 ∧ f b = 0) (h₂ : a ≠ b) (h₃ : Nat.Prime a ∧ Nat.Prime b) : k = 122 := by
  sorry

Runs (0)

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