Theorems · Theorem · number theory
Nat.totient_eq_prod_factorization
∀ {n : ℕ}, n ≠ 0 → n.totient = n.factorization.prod fun p k => p ^ (k - 1) * (p - 1)Euler's product formula for the totient function.
- Defined in
- Mathlib.Data.Nat.Totient
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsupp.supportproof · cited by 828
- Finsupp.prodstatement and proof · cited by 231
- Nat.factorizationstatement and proof · cited by 215
- Nat.totientstatement and proof · cited by 111
- Finsupp.mem_support_iffproof · cited by 89
- Nat.prime_of_mem_primeFactorsproof · cited by 29
- zero_lt_iffproof · cited by 29
- Nat.totient_prime_powproof · cited by 13
- Finsupp.prod_congrproof · cited by 6
- Nat.totient_mulproof · cited by 5
- Nat.totient_oneproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Nat.totient_dvd_of_dvdproof · cited by 2
- Nat.totient_mul_prod_primeFactorsproof · cited by 1