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riccardobrasca committed Dec 5, 2024
1 parent 8f1fef9 commit 8973978
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3 changes: 2 additions & 1 deletion FltRegular/NumberTheory/KummersLemma/KummersLemma.lean
Original file line number Diff line number Diff line change
Expand Up @@ -47,6 +47,7 @@ theorem not_for_all_zeta_sub_one_pow_dvd_sub_one_of_pow_ne (u : (π“ž K)Λ£)
-- the 𝑝-th cyclotomic field) and πœ‰ a primitive 𝑝-th root of unity;
-- if a unit π‘’βˆˆπ(πœ‰) is congruent to an integer modulo 𝑝, then 𝑒 is a 𝑝-th power in 𝐐(πœ‰).
set_option synthInstance.maxHeartbeats 40000 in
set_option maxHeartbeats 400000 in
theorem eq_pow_prime_of_unit_of_congruent (u : (π“ž K)Λ£)
(hcong : βˆƒ n : β„€, (p : π“ž K) ∣ (u - n : π“ž K)) :
βˆƒ v, u = v ^ (p : β„•) := by
Expand All @@ -55,7 +56,7 @@ theorem eq_pow_prime_of_unit_of_congruent (u : (π“ž K)Λ£)
obtain ⟨x, hx⟩ : (p : π“ž K) ∣ (↑(u ^ (p - 1 : β„•)) : π“ž K) - 1 := by
obtain ⟨n, hn⟩ := hcong
have hn' : (p : β„€) ∣ n ^ (p - 1 : β„•) - 1 := by
refine Int.modEq_iff_dvd.mp (Int.ModEq.pow_card_sub_one_eq_one hpri.out (n := n) ?_).symm
refine Int.modEq_iff_dvd.mp (Int.ModEq.pow_card_sub_one_eq_one hpri.out ?_).symm
rw [isCoprime_comm, (Nat.prime_iff_prime_int.mp hpri.out).coprime_iff_not_dvd]
intro h
replace h := _root_.map_dvd (Int.castRingHom (π“ž K)) h
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6 changes: 3 additions & 3 deletions lake-manifest.json
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Expand Up @@ -15,7 +15,7 @@
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Expand All @@ -25,7 +25,7 @@
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Expand Down Expand Up @@ -135,7 +135,7 @@
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