Theorems · Theorem · number theory
emultiplicity_pow_prime_pow_sub_pow_prime_pow
∀ {R : Type u_1} [inst : CommRing R] {x y : R} {p : ℕ} [IsDomain R],
Prime ↑p →
Odd p →
↑p ∣ x - y → ¬↑p ∣ x → ∀ (a : ℕ), emultiplicity (↑p) (x ^ p ^ a - y ^ p ^ a) = emultiplicity (↑p) (x - y) + ↑a- Defined in
- Mathlib.NumberTheory.Multiplicity
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Finset.sumproof · cited by 5,195
- ENatstatement and proof · cited by 4,985
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- IsDomainstatement and proof · cited by 2,196
- Nat.cast_zeroproof · cited by 1,870
- Finset.rangeproof · cited by 1,341
- pow_zeroproof · cited by 1,094
- pow_oneproof · cited by 894
- add_assocproof · cited by 746
- Nat.cast_addproof · cited by 586
Cited by1
Results whose statement or proof uses this declaration.
- Int.emultiplicity_pow_sub_powproof · cited by 2