Theorems · Theorem · field theory
X_pow_sub_C_irreducible_iff_forall_prime_of_odd
∀ {K : Type u} [inst : Field K] {n : ℕ},
Odd n →
∀ {a : K}, Irreducible (Polynomial.X ^ n - Polynomial.C a) ↔ ∀ (p : ℕ), Nat.Prime p → p ∣ n → ∀ (b : K), b ^ p ≠ a- Defined in
- Mathlib.FieldTheory.KummerExtension
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- Nat.Primestatement and proof · cited by 2,059
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Irreduciblestatement and proof · cited by 496
- Oddstatement and proof · cited by 364
- Nat.Prime.ne_oneproof · cited by 61
- pow_ne_of_irreducible_X_pow_sub_Cproof · cited by 4
- X_pow_sub_C_irreducible_of_oddproof · cited by 3
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