fix(NumberTheory/Carmichael): definition and import#4281
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making sure the definition and the docstring are aligned and fixing making the import more specific |
danielchin
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Jun 18, 2026
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Looks a lot cleaner and I prefer this organization a lot more. LGTM
YaelDillies
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| /-- A composite Carmichael number is squarefree. -/ | ||
| @[category textbook, AMS 11] | ||
| theorem squarefree_of_isCarmichael {a : ℕ} (ha₁ : a.Composite) (ha₂ : IsCarmichael a) : | ||
| Squarefree a := by | ||
| have ha₂_forall := ha₂ | ||
| simp_all [IsCarmichael, Nat.Composite, a.squarefree_iff_prime_squarefree, Nat.FermatPsp, Nat.ProbablePrime] | ||
| rintro p hp ⟨N, rfl⟩ | ||
| apply absurd (ha₂_forall (p * N + 1) ((1).le_add_left _)) | ||
| have : Fact p.Prime := ⟨hp⟩ | ||
| rw [mul_assoc] at ha₁ | ||
| rw [mul_assoc, ← geom_sum_mul_of_one_le ((1).le_add_left (p * N)), p.coprime_mul_iff_left] | ||
| simpa using (mul_dvd_mul_iff_right fun _ ↦ by simp_all only [mul_zero, not_lt_zero']).not.mpr | ||
| ((ZMod.natCast_eq_zero_iff _ _).not.mp (by simp [le_of_lt ha₁.1])) | ||
| theorem squarefree_of_isCarmichael {a : ℕ} (_ha₁ : a.Composite) (ha₂ : IsCarmichael a) : |
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Surely you don't need the compositeness assumption?
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