Theorems · Theorem · number theory
Int.emultiplicity_pow_sub_pow
∀ {p : ℕ},
Nat.Prime p →
Odd p →
∀ {x y : ℤ},
↑p ∣ x - y →
¬↑p ∣ x → ∀ (n : ℕ), emultiplicity (↑p) (x ^ n - y ^ n) = emultiplicity (↑p) (x - y) + emultiplicity p nLifting the exponent lemma for odd primes.
- Defined in
- Mathlib.NumberTheory.Multiplicity
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- ENatstatement and proof · cited by 4,985
- Nat.Primestatement and proof · cited by 2,059
- mul_assocproof · cited by 1,667
- pow_zeroproof · cited by 1,094
- sub_selfproof · cited by 996
- pow_succproof · cited by 374
- Oddstatement and proof · cited by 364
- pow_mulproof · cited by 210
- emultiplicitystatement and proof · cited by 156
- multiplicityproof · cited by 117
- FiniteMultiplicityproof · cited by 73
Cited by2
Results whose statement or proof uses this declaration.
- Nat.emultiplicity_pow_sub_powproof · cited by 1
- Int.emultiplicity_pow_add_powproof · cited by 1