Theorems · Theorem · number theory
Nat.infinite_setOf_prime_and_eq_mod
Deprecated since 2026-07-09Use Nat.infinite_setOfPred_prime_and_eq_mod instead.
- 1000+ list: Dirichlet's theorem on arithmetic progressions
∀ {q : ℕ} [NeZero q] {a : ZMod q}, IsUnit a → {p | Nat.Prime p ∧ ↑p = a}.InfiniteAlias of Nat.infinite_setOfPred_prime_and_eq_mod.
Dirichlet'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
- 0 results in Mathlib
- Foundations
- Depth 323 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredstatement · cited by 6,101
- Nat.Primestatement · cited by 2,059
- IsUnitstatement · cited by 1,602
- ZModstatement · cited by 1,024
- Set.Infinitestatement · cited by 263
- Nat.infinite_setOfPred_prime_and_eq_modproof · cited by 2
Cited by0
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