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[Merged by Bors] - feat: Polynomial FLT #18882

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Merge pull request #19018 from leanprover-community/feature/poly-flt-…
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4 changes: 1 addition & 3 deletions Mathlib/NumberTheory/FLT/Polynomial.lean
Original file line number Diff line number Diff line change
Expand Up @@ -21,6 +21,7 @@ More generally, we can prove non-solvability of the Fermat-Catalan equation: the
non-constant polynomial solution of the equation `u * a ^ p + v * b ^ q + w * c ^ r = 0`, where
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`p, q, r ≥ 3` with `p * q + q * r + r * p ≤ p * q * r` and not divisible by `char k`
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and `u, v, w` are nonzero elements in `k`.
FLT is special case when `p = q = r = n`, `u = v = 1`, and `w = -1`.
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The proof uses the Mason-Stothers theorem (Polynomial ABC theorem) and infinite descent
(in the characteristic p case).
Expand Down Expand Up @@ -214,9 +215,6 @@ theorem Polynomial.flt_catalan
rw [← mul_rotate] at hineq
apply flt_catalan_aux heq <;> assumption

/- FLT is special case of nonsolvability of Fermat-Catalan equation.
Take p = q = r = n and u = v = 1, w = -1.
-/
theorem Polynomial.flt
{n : ℕ} (hn : 3 ≤ n) (chn : (n : k) ≠ 0)
{a b c : k[X]} (ha : a ≠ 0) (hb : b ≠ 0) (hc : c ≠ 0)
Expand Down
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