Theorems · Theorem · number theory
ArithmeticFunction.IsMultiplicative.map_gcd
∀ {R : Type u_1} [inst : CommGroupWithZero R] {f : ArithmeticFunction R},
f.IsMultiplicative → ∀ {x y : ℕ}, f (x.lcm y) ≠ 0 → f (x.gcd y) = f x * f y / f (x.lcm y)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommGroupWithZero
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Cites6
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
- ArithmeticFunctionstatement and proof · cited by 290
- mul_div_cancel_left₀proof · cited by 111
- CommGroupWithZerostatement and proof · cited by 94
- ArithmeticFunction.IsMultiplicativestatement and proof · cited by 45
- ArithmeticFunction.IsMultiplicative.lcm_apply_mul_gcd_applyproof · cited by 2
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