Theorems · Theorem · commutative algebra

Commute.add_pow_prime_pow_eq

∀ {R : Type u_1} [inst : Semiring R] {p : ℕ},
  Nat.Prime p →
    ∀ {x y : R},
      Commute x y →
        ∀ (n : ℕ),
          (x + y) ^ p ^ n =
            x ^ p ^ n + y ^ p ^ n +
              ↑p * x * y * ∑ k ∈ Finset.Ioo 0 (p ^ n), x ^ (k - 1) * y ^ (p ^ n - k - 1) * ↑((p ^ n).choose k / p)

Defined in

Mathlib.Algebra.CharP.Lemmas

Cited by

3 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Semiring