Theorems · Theorem · number theory
schnirelmannDensity_setOfPred_mod_eq_one
∀ {m : ℕ}, m ≠ 1 → schnirelmannDensity {n | n % m = 1} = (↑m)⁻¹The Schnirelmann density of the set of naturals which are 1 mod m is m⁻¹, for any m ≠ 1.
Note that if m = 1, this set is empty.
- Defined in
- Mathlib.Combinatorics.Schnirelmann
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Set.ofPredstatement and proof · cited by 6,101
- Nat.cast_oneproof · cited by 2,501
- Finset.cardproof · cited by 2,327
- mul_commproof · cited by 2,262
- le_antisymmproof · cited by 2,068
- Nat.cast_zeroproof · cited by 1,870
- Set.Finiteproof · cited by 1,814
- LT.lt.ne'proof · cited by 1,417
- le_of_ltproof · cited by 1,175
- Finset.filterproof · cited by 949
- Finset.imageproof · cited by 910
Cited by3
Results whose statement or proof uses this declaration.
- schnirelmannDensity_setOfPred_modeq_oneproof · cited by 1
- schnirelmannDensity_setOfPred_Oddproof · cited by 1
- schnirelmannDensity_setOf_mod_eq_oneproof · cited by 0