Theorems · Theorem · number theory
Polynomial.cyclotomic_coeff_zero
∀ (R : Type u_1) [inst : CommRing R] {n : ℕ}, 1 < n → (Polynomial.cyclotomic n R).coeff 0 = 1The constant term of cyclotomic n R is 1 if 2 ≤ n.
- Cited by
- 3 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.
Cites49
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
- Finsetproof · cited by 13,712
- Polynomialproof · cited by 5,681
- mul_oneproof · cited by 3,885
- Finset.prodproof · cited by 2,356
- Polynomial.Xproof · cited by 1,639
- Polynomial.coeffstatement and proof · cited by 1,045
- LE.le.trans_ltproof · cited by 795
- Finset.prod_congrproof · cited by 646
- ne_of_gtproof · cited by 637
- mul_negproof · cited by 590
- MonoidWithZeroproof · cited by 456
Cited by3
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.norm_eq_oneproof · cited by 3
- Polynomial.coprime_of_root_cyclotomicproof · cited by 2
- Polynomial.sub_one_pow_totient_lt_natAbs_cyclotomic_evalproof · cited by 1