Theorems · Theorem · number theory
Nat.two_pow_sub_pow
∀ {x y : ℕ},
2 ∣ x - y →
¬2 ∣ x →
∀ {n : ℕ},
Even n →
emultiplicity 2 (x ^ n - y ^ n) + 1 = emultiplicity 2 (x + y) + emultiplicity 2 (x - y) + emultiplicity 2 n- Defined in
- Mathlib.NumberTheory.Multiplicity
- Cited by
- 1 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.
Cites11
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
- Evenstatement and proof · cited by 444
- le_totalproof · cited by 294
- emultiplicitystatement and proof · cited by 156
- top_addproof · cited by 55
- add_topproof · cited by 49
- pow_le_pow_left'proof · cited by 25
- emultiplicity_zeroproof · cited by 10
- Int.natCast_emultiplicityproof · cited by 7
- Int.two_pow_sub_powproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- padicValNat.pow_two_sub_powproof · cited by 1