induction k
n a b : ℤ
k : ℕ
h : a ≡ b [ZMOD n]
⊢ a ^ k ≡ b ^ k [ZMOD n]
case zero
n a b : ℤ
h : a ≡ b [ZMOD n]
⊢ a ^ Nat.zero ≡ b ^ Nat.zero [ZMOD n]

case succ
n a b : ℤ
h : a ≡ b [ZMOD n]
n✝ : ℕ
n_ih✝ : a ^ n✝ ≡ b ^ n✝ [ZMOD n]
⊢ a ^ Nat.succ n✝ ≡ b ^ Nat.succ n✝ [ZMOD n]