Theorems · Theorem · number theory
Nat.succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul
∀ {p : ℕ},
Nat.Prime p → ∀ {m n k l : ℕ}, p ^ k ∣ m → p ^ l ∣ n → p ^ (k + l + 1) ∣ m * n → p ^ (k + 1) ∣ m ∨ p ^ (l + 1) ∣ n- Defined in
- Mathlib.Data.Nat.Prime.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 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.
- Nat.Primestatement and proof · cited by 2,059
- pow_succproof · cited by 374
- pow_addproof · cited by 315
- Nat.Prime.dvd_mulproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- Int.succ_dvd_or_succ_dvd_of_succ_sum_dvd_mulproof · cited by 0