Theorems · Definition · number theory
ZMod.chineseRemainder
- 1000+ list: Chinese remainder theorem
{m n : ℕ} → m.Coprime n → ZMod (m * n) ≃+* ZMod m × ZMod nThe Chinese remainder theorem. For a pair of coprime natural numbers, m and n,
the rings ZMod (m * n) and ZMod m × ZMod n are isomorphic.
See Ideal.quotientInfRingEquivPiQuotient for the Chinese remainder theorem for ideals in any
ring.
- Defined in
- Mathlib.Data.ZMod.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingEquivstatement · cited by 1,147
- ZModstatement and proof · cited by 1,024
- ZMod.valproof · cited by 159
- ZMod.castproof · cited by 87
- ZMod.castHomproof · cited by 55
- RingHom.sndproof · cited by 39
- RingHom.fstproof · cited by 36
- Nat.chineseRemainderproof · cited by 7
Cited by6
Results whose statement or proof uses this declaration.
- Nat.totient_mulproof · cited by 5
- ZMod.isSquare_neg_one_mulproof · cited by 1
- ZMod.isCyclic_units_four_mul_iffproof · cited by 1
- ZMod.not_isCyclic_units_of_mul_coprimeproof · cited by 1
- ZMod.isCyclic_units_two_mul_iff_of_oddproof · cited by 1
- ZMod.chineseRemainder.congr_simpstatement and proof · cited by 0