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theorem proved term proof

sigma_mul_of_coprime

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formal statement (Lean)

 769theorem sigma_mul_of_coprime {k m n : ℕ} (h : Nat.Coprime m n) :
 770    sigma k (m * n) = sigma k m * sigma k n := by

proof body

Term-mode proof.

 771  simp only [sigma]
 772  exact ArithmeticFunction.isMultiplicative_sigma.map_mul_of_coprime h
 773
 774/-- σ_0(mn) = σ_0(m) × σ_0(n) for coprime m, n. -/

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