Theorems · Theorem · number theory
FiniteField.sum_subgroup_pow_eq_zero
∀ {K : Type u_1} [inst : CommRing K] [NoZeroDivisors K] {G : Subgroup Kˣ} [inst_2 : Fintype ↥G] {k : ℕ},
k ≠ 0 → k < Fintype.card ↥G → ∑ x, ↑↑x ^ k = 0- Defined in
- Mathlib.FieldTheory.Finite.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
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- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Subgroupstatement and proof · cited by 3,593
- Finset.univstatement and proof · cited by 3,473
- one_mulproof · cited by 2,841
- Unitsstatement and proof · cited by 2,804
- Multisetproof · cited by 2,627
- Nontrivialproof · cited by 2,416
- mul_commproof · cited by 2,262
- IsDomainproof · cited by 2,196
- Units.valstatement and proof · cited by 1,966
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