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[Merged by Bors] - refactor(NumberTheory): golf Mathlib/NumberTheory/PellMatiyasevic #38494

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[Merged by Bors] - refactor(NumberTheory): golf Mathlib/NumberTheory/PellMatiyasevic #38494

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83d958a
refactor(NumberTheory): golf PellMatiyasevic
yuanyi-350 Apr 25, 2026
1c154ec
Update PellMatiyasevic.lean
yuanyi-350 Apr 25, 2026
9ee2889
Update Mathlib/NumberTheory/PellMatiyasevic.lean
yuanyi-350 Apr 27, 2026
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9 changes: 1 addition & 8 deletions Mathlib/NumberTheory/PellMatiyasevic.lean
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Expand Up @@ -466,16 +466,9 @@ theorem dvd_of_ysq_dvd {n t} (h : yn a1 n * yn a1 n ∣ yn a1 t) : yn a1 n ∣ t
rw [ke]
exact dvd_mul_of_dvd_right (((xy_coprime _ _).pow_left _).symm.dvd_of_dvd_mul_right this) _

set_option backward.isDefEq.respectTransparency false in
theorem pellZd_succ_succ (n) :
pellZd a1 (n + 2) + pellZd a1 n = (2 * a : ℕ) * pellZd a1 (n + 1) := by
have : (1 : ℤ√(d a1)) + ⟨a, 1⟩ * ⟨a, 1⟩ = ⟨a, 1⟩ * (2 * a) := by
rw [Zsqrtd.natCast_val]
change (⟨_, _⟩ : ℤ√(d a1)) = ⟨_, _⟩
rw [dz_val]
dsimp [az]
ext <;> dsimp <;> ring_nf
simpa [mul_add, mul_comm, mul_left_comm, add_comm] using congr_arg (· * pellZd a1 n) this
ext <;> simp [dz_val, az] <;> ring_nf

theorem xy_succ_succ (n) :
xn a1 (n + 2) + xn a1 n =
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