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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
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