Theorems · Theorem · number theory
Polynomial.cyclotomic.irreducible_rat
∀ {n : ℕ}, 0 < n → Irreducible (Polynomial.cyclotomic n ℚ)cyclotomic n ℚ is irreducible.
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Polynomialstatement and proof · cited by 5,681
- Irreduciblestatement and proof · cited by 496
- Polynomial.cyclotomicstatement · cited by 130
- Polynomial.map_cyclotomic_intproof · cited by 21
- Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_mapproof · cited by 4
- Polynomial.cyclotomic.isPrimitiveproof · cited by 2
- Polynomial.cyclotomic.irreducibleproof · cited by 1
Cited by18
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.finrankproof · cited by 4
- IsCyclotomicExtension.Rat.nrComplexPlaces_eq_totient_div_twoproof · cited by 4
- IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_pow_ne_twoproof · cited by 3
- IsPrimitiveRoot.norm_toInteger_sub_one_of_eq_two_powproof · cited by 2
- IsCyclotomicExtension.Rat.discr_prime_powproof · cited by 2
- IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_twoproof · cited by 1
- IsPrimitiveRoot.norm_toInteger_sub_one_eq_oneproof · cited by 1
- IsCyclotomicExtension.Rat.discr_prime_pow_eq_unit_mul_pow'proof · cited by 1
- IsPrimitiveRoot.zeta_sub_one_prime_of_ne_twoproof · cited by 1
- IsPrimitiveRoot.zeta_sub_one_prime_of_two_powproof · cited by 1
- Polynomial.cyclotomic.isCoprime_ratproof · cited by 1