Theorems · Theorem · number theory
Nat.infinite_setOfPred_prime_and_eq_mod
- #48 of the 100 theorems: Dirichlet’s Theorem
∀ {q : ℕ} [NeZero q] {a : ZMod q}, IsUnit a → {p | Nat.Prime p ∧ ↑p = a}.InfiniteDirichlet's Theorem on primes in arithmetic progression: if q is a positive
integer and a : ZMod q is a unit, then there are infinitely many prime numbers p
such that (p : ZMod q) = a.
- Defined in
- Mathlib.NumberTheory.LSeries.PrimesInAP
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 322 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredstatement and proof · cited by 6,101
- Nat.Primestatement and proof · cited by 2,059
- Set.Finiteproof · cited by 1,814
- IsUnitstatement and proof · cited by 1,602
- ZModstatement and proof · cited by 1,024
- Function.supportproof · cited by 610
- Set.Infinitestatement and proof · cited by 263
- ArithmeticFunction.vonMangoldt.residueClassproof · cited by 14
- summable_of_hasFiniteSupportproof · cited by 12
- ArithmeticFunction.vonMangoldt.not_summable_residueClass_prime_divproof · cited by 1
- ArithmeticFunction.vonMangoldt.support_residueClass_prime_divproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Nat.forall_exists_prime_gt_and_eq_modproof · cited by 1
- Nat.infinite_setOf_prime_and_eq_modproof · cited by 0