Theorems · Theorem · number theory
geom_sum_eq_zero_iff_neg_one
∀ {R : Type u_1} [inst : Ring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {n : ℕ} {x : R},
n ≠ 0 → (∑ i ∈ Finset.range n, x ^ i = 0 ↔ x = -1 ∧ Even n)- Defined in
- Mathlib.Algebra.Order.Ring.GeomSum
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- Finset.sumstatement and proof · cited by 5,195
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Finset.sum_congrproof · cited by 2,323
- Finset.rangestatement and proof · cited by 1,341
- eq_or_neproof · cited by 1,117
- Evenstatement and proof · cited by 444
- neg_one_geom_sumproof · cited by 4
- geom_sum_ne_zeroproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.cyclotomic_posproof · cited by 1
- geom_sum_neg_iffproof · cited by 1