Theorems · Theorem · number theory
Nat.sum_properDivisors_eq_one_iff_prime
∀ {n : ℕ}, ∑ x ∈ n.properDivisors, x = 1 ↔ Nat.Prime n- Defined in
- Mathlib.NumberTheory.Divisors
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finset.sumstatement and proof · cited by 5,195
- zero_addproof · cited by 2,366
- Finset.sum_congrproof · cited by 2,323
- Nat.Primestatement and proof · cited by 2,059
- Finset.sum_singletonproof · cited by 251
- Nat.properDivisorsstatement and proof · cited by 52
- Finset.singleton_subset_iffproof · cited by 38
- Nat.properDivisors_zeroproof · cited by 6
- Nat.one_mem_properDivisors_iff_one_ltproof · cited by 4
- Nat.properDivisors_oneproof · cited by 2
- Nat.eq_properDivisors_of_subset_of_sum_eq_sumproof · cited by 2
- Nat.properDivisors_eq_singleton_one_iff_primeproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Nat.Prime.not_abundantproof · cited by 0