Theorems · Theorem · number theory
Int.gcd_dvd_iff
∀ {a b : ℤ} {n : ℕ}, a.gcd b ∣ n ↔ ∃ x y, ↑n = a * x + b * y- Defined in
- Mathlib.Data.Int.GCD
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_assocproof · cited by 1,667
- Int.gcdAproof · cited by 7
- Int.gcdBproof · cited by 7
- Int.gcd_eq_gcd_abproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Int.isCoprime_iff_gcd_eq_oneproof · cited by 16
- Nat.exists_add_mul_eq_of_gcd_dvd_of_mul_pred_leproof · cited by 3
- mem_zmultiples_zsmul_iffproof · cited by 1