Theorems · Theorem · number theory
Polynomial.cyclotomic.isCoprime_rat
∀ {n m : ℕ}, n ≠ m → IsCoprime (Polynomial.cyclotomic n ℚ) (Polynomial.cyclotomic m ℚ)If n ≠ m, then (cyclotomic n ℚ) and (cyclotomic m ℚ) are coprime.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 211 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.
- Polynomialstatement · cited by 5,681
- IsCoprimestatement · cited by 321
- Polynomial.cyclotomicstatement and proof · cited by 130
- Polynomial.cyclotomic.irreducible_ratproof · cited by 18
- Polynomial.cyclotomic.monicproof · cited by 12
- Polynomial.eq_of_monic_of_associatedproof · cited by 8
- isCoprime_one_leftproof · cited by 8
- Irreducible.associated_of_dvdproof · cited by 6
- Irreducible.coprime_iff_not_dvdproof · cited by 5
- isCoprime_one_rightproof · cited by 5
- Polynomial.cyclotomic_injectiveproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.cyclotomic_expand_eq_cyclotomic_mulproof · cited by 2