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Theorems · Theorem · number theory

ArithmeticFunction.IsMultiplicative.map_lcm

∀ {R : Type u_1} [inst : CommGroupWithZero R] {f : ArithmeticFunction R},
  f.IsMultiplicative → ∀ {x y : ℕ}, f (x.gcd y) ≠ 0 → f (x.lcm y) = f x * f y / f (x.gcd y)
Defined in
Mathlib.NumberTheory.ArithmeticFunction.Defs
Cited by
1 results in Mathlib
Foundations
Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommGroupWithZero
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Around this declaration

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BoundingSieve.mainSum_lambdaSquared_eq_sum_sum_mul · cited by 1BoundingSieve.mainSum_lam…DFunLike.coe · cited by 62936DFunLike.coeArithmeticFunction · cited by 290ArithmeticFunctionCommGroupWithZero · cited by 94CommGroupWithZeromul_div_cancel_right₀ · cited by 70mul_div_cancel_right₀ArithmeticFunction.IsMultiplicative · cited by 45ArithmeticFunction.IsMult…ArithmeticFunction.IsMultiplicative.lcm_apply_mul_gcd_apply · cited by 2IsMultiplicative.lcm_appl…IsMultiplicative.map_lcmCITED BYCITES

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