Theorems · Theorem · number theory
Irreducible.natDegree_dvd_of_dvd_X_pow_card_pow_sub_X
∀ {k : Type u_1} [inst : Field k] {f : Polynomial k},
Irreducible f → ∀ {n : ℕ}, f ∣ Polynomial.X ^ Nat.card k ^ n - Polynomial.X → f.natDegree ∣ n- Defined in
- Mathlib.FieldTheory.Finite.Extension
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- Finiteproof · cited by 3,029
- Factproof · cited by 2,726
- Nat.Primeproof · cited by 2,059
- Polynomial.Xstatement and proof · cited by 1,639
- eq_or_neproof · cited by 1,117
- Polynomial.natDegreestatement and proof · cited by 1,105
- pow_zeroproof · cited by 1,094
- Nat.cardstatement and proof · cited by 844
- Irreduciblestatement and proof · cited by 496
Cited by1
Results whose statement or proof uses this declaration.
- Irreducible.natDegree_dvd_iff_dvd_X_pow_card_pow_sub_Xproof · cited by 0