Theorems · Theorem · ring theory
Commute.sub_dvd_pow_sub_pow
∀ {R : Type u_1} [inst : Ring R] {x y : R}, Commute x y → ∀ (n : ℕ), x - y ∣ x ^ n - y ^ n- Defined in
- Mathlib.Algebra.Ring.GeomSum
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Finset.sumproof · cited by 5,195
- Finset.rangeproof · cited by 1,341
- Commutestatement and proof · cited by 639
- Dvd.introproof · cited by 26
- Commute.mul_geom_sum₂proof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- sub_dvd_pow_sub_powproof · cited by 4
- sub_one_dvd_pow_sub_oneproof · cited by 2
- one_sub_dvd_one_sub_powproof · cited by 1
- exists_isIdempotentElem_mul_eq_zero_of_ker_isNilpotent_auxproof · cited by 1