Theorems · Theorem · number theory
Nat.forall_exists_prime_gt_and_zmodEq
∀ (n : ℕ) {q : ℕ} {a : ℤ}, q ≠ 0 → IsCoprime a ↑q → ∃ p > n, Nat.Prime p ∧ ↑p ≡ a [ZMOD ↑q]Dirichlet's Theorem on primes in arithmetic progression: if q is a positive
integer and a : ℤ is coprime to q, then there are infinitely many prime numbers p
such that p ≡ a mod q.
- Defined in
- Mathlib.NumberTheory.LSeries.PrimesInAP
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 324 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- IsUnitproof · cited by 1,602
- Int.cast_natCastproof · cited by 393
- IsCoprimestatement and proof · cited by 321
- Int.ModEqstatement · cited by 147
- isCoprime_commproof · cited by 17
- ZMod.coe_int_isUnit_iff_isCoprimeproof · cited by 2
- Nat.forall_exists_prime_gt_and_eq_modproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Nat.forall_exists_prime_gt_and_modEqproof · cited by 1