Theorems · Theorem · number theory
IsPrimitiveRoot.sub_one_dvd_natCast
∀ {n : ℕ} {A : Type u_1} {ζ : A} [inst : CommRing A] [IsDomain A], IsPrimitiveRoot ζ n → 1 < n → ζ - 1 ∣ ↑nGiven an n-th primitive root of unity ζ, where 1 < n, we have that ζ - 1 divides n.
In particular, if ζ is a p-th primitive root of unity with p prime, then ζ - 1 divides
p.
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- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites6
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- CommRingstatement and proof · cited by 17,173
- IsDomainstatement and proof · cited by 2,196
- IsPrimitiveRootstatement and proof · cited by 356
- IsPrimitiveRoot.pow_eq_oneproof · cited by 48
- IsPrimitiveRoot.ne_oneproof · cited by 7
- sub_one_dvd_natCast_of_pow_eq_oneproof · cited by 1
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