Theorems · Theorem · number theory
Polynomial.prod_cyclotomic_eq_geom_sum
∀ {n : ℕ},
0 < n →
∀ (R : Type u_1) [inst : CommRing R],
∏ i ∈ n.divisors.erase 1, Polynomial.cyclotomic i R = ∑ i ∈ Finset.range n, Polynomial.X ^ i- Cited by
- 4 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- Finset.sumstatement and proof · cited by 5,195
- Finset.prodstatement and proof · cited by 2,356
- Finset.sum_congrproof · cited by 2,323
- Polynomial.Xstatement and proof · cited by 1,639
- LT.lt.ne'proof · cited by 1,417
- Finset.rangestatement and proof · cited by 1,341
- Polynomial.mapproof · cited by 806
- Finset.prod_congrproof · cited by 646
- Finset.erasestatement and proof · cited by 455
- Int.castRingHomproof · cited by 254
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.cyclotomic_primeproof · cited by 7
- Polynomial.eval_one_cyclotomic_not_prime_powproof · cited by 1
- Polynomial.cyclotomic_posproof · cited by 1
- Polynomial.cyclotomic_dvd_geom_sum_of_dvdproof · cited by 0