Theorems · Theorem · number theory
MvPolynomial.C_dvd_iff_zmod
∀ {σ : Type u_1} (n : ℕ) (φ : MvPolynomial σ ℤ),
MvPolynomial.C ↑n ∣ φ ↔ (MvPolynomial.map (Int.castRingHom (ZMod n))) φ = 0A polynomial over the integers is divisible by n : ℕ
if and only if it is zero over ZMod n.
- Defined in
- Mathlib.FieldTheory.Finite.Polynomial
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement · cited by 10,189
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- ZModstatement and proof · cited by 1,024
- MvPolynomial.Cstatement · cited by 400
- Int.castRingHomstatement and proof · cited by 254
- MvPolynomial.mapstatement · cited by 147
- CharP.intCast_eq_zero_iffproof · cited by 7
- MvPolynomial.C_dvd_iff_map_hom_eq_zeroproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sumproof · cited by 1