Theorems · Theorem · number theory
ArithmeticFunction.liouville_apply_mul
∀ (m n : ℕ), ArithmeticFunction.liouville (m * n) = ArithmeticFunction.liouville m * ArithmeticFunction.liouville n
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- pow_addproof · cited by 315
- ArithmeticFunctionstatement · cited by 290
- ArithmeticFunction.map_zeroproof · cited by 34
- ArithmeticFunction.cardFactorsproof · cited by 22
- ArithmeticFunction.cardFactors_mulproof · cited by 6
- ArithmeticFunction.liouvillestatement and proof · cited by 5
- ArithmeticFunction.liouville_applyproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- ArithmeticFunction.isMultiplicative_liouvilleproof · cited by 0