| import Mathlib | |
| open Nat | |
| theorem imo_1959_p1 | |
| (n : ℕ) | |
| (h₀ : 0 < n) : | |
| Nat.gcd (21*n + 4) (14*n + 3) = 1 := by | |
| have h₁: Nat.gcd (21*n + 4) (14*n + 3) = Nat.gcd (7*n + 1) (14*n + 3) := by | |
| have g₀: (21 * n + 4) = (7*n + 1) + 1 * (14 * n + 3) := by linarith | |
| rw [g₀] | |
| exact gcd_add_mul_right_left (7 * n + 1) (14 * n + 3) 1 | |
| have h₂: Nat.gcd (7*n + 1) (14*n + 3) = Nat.gcd (7*n + 1) (1) := by | |
| have g₁: 14 * n + 3 = (7 * n + 1) * 2 + 1 := by linarith | |
| rw [g₁] | |
| exact gcd_mul_left_add_right (7 * n + 1) 1 2 | |
| have h₃: Nat.gcd (7*n + 1) (1) = 1 := by | |
| exact Nat.gcd_one_right (7 * n + 1) | |
| linarith | |