Theorems · Theorem · number theory
gcd_nsmul_eq_zero
∀ {M : Type u_1} [inst : AddMonoid M] {a : M} {m n : ℕ}, m.gcd n • a = 0 ↔ m • a = 0 ∧ n • a = 0- Defined in
- Mathlib.Data.Int.GCD
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Quot.sound
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- zero_addproof · cited by 2,366
- AddUnitsproof · cited by 325
- AddUnits.valproof · cited by 248
- natCast_zsmulproof · cited by 118
- nsmul_zeroproof · cited by 73
- mul_nsmulproof · cited by 24
- Nat.gcdAproof · cited by 23
- add_zsmulproof · cited by 21
- Nat.gcdBproof · cited by 21
- mul_zsmul'proof · cited by 16
- zsmul_zeroproof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- IsAddCyclic.card_nsmul_eq_zero_leproof · cited by 1
- nsmul_eq_zero_iff_of_coprimeproof · cited by 0
- intGCD_nsmul_eq_zeroproof · cited by 0