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riccardobrasca committed Mar 4, 2024
1 parent 81513b0 commit d9a41fc
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26 changes: 2 additions & 24 deletions FltRegular/FLT5.lean
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Expand Up @@ -5,31 +5,9 @@ open Nat NumberField Polynomial IsPrimitiveRoot IsCyclotomicExtension Real Compl
open scoped nonZeroDivisors

theorem fermatLastTheoremFive : FermatLastTheoremFor 5 := by
classical
have five_pos : 0 < 5 := by norm_num
let p := (⟨5, five_pos⟩ : ℕ+)
have hφ : φ 5 = 4 := rfl
have : Fact (Nat.Prime 5) := ⟨by norm_num⟩
have hodd : 52 := by omega
have hp : Fact (Nat.Prime (↑p : ℕ)) := this
let K := CyclotomicField p ℚ

refine flt_regular ?_ hodd
refine flt_regular ?_ (by omega)
rw [IsRegularPrime, IsRegularNumber]
convert coprime_one_right _
refine classNumber_eq_one_iff.2 (RingOfIntegers.isPrincipalIdealRing_of_abs_discr_lt ?_)
suffices : discr K = 125
rw [IsCyclotomicExtension.finrank (n := 5) K (cyclotomic.irreducible_rat five_pos), this]
· suffices InfinitePlace.NrComplexPlaces K = 2 by
· rw [this, show ((5 : ℕ+) : ℕ) = 5 by rfl, hφ, show ((4! : ℕ) : ℝ) = 24 by rfl,
abs_of_pos (by norm_num)]
norm_num
suffices (2 * (3 ^ 2 / 16) * (32 / 3)) ^ 2 < (2 * ((π : ℝ) ^ 2 / 16) * (32 / 3)) ^ 2 by
· refine lt_trans ?_ this
norm_num
gcongr
exact pi_gt_three
rw [Rat.nrComplexPlaces_eq_totient_div_two (n := 5)]
rfl
· convert IsCyclotomicExtension.Rat.absdiscr_prime p K
assumption
exact classNumber_eq_one_iff.2 (Rat.five_pid (CyclotomicField _ ℚ))
2 changes: 1 addition & 1 deletion lake-manifest.json
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Expand Up @@ -58,7 +58,7 @@
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"type": "git",
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"rev": "86b7828a1e4debe4984e5051220a6026c8d4c6a1",
"rev": "1095e9af4d1f75960ab5485a6c5b3a851f48b5f4",
"name": "mathlib",
"manifestFile": "lake-manifest.json",
"inputRev": null,
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