Bennett two clear column two
ProvedD1Bound5.bennett_two_clear_column_twodiophantine-tuplesnumber-theory
Column two of the two-anchor construction, with its exact b^k divisibility and every surviving nonnegative difference exponent.
Preamble
import Lean.Elab.Tactic.Omega import Mathlib.Algebra.Polynomial.BigOperators import Mathlib.Algebra.Polynomial.Degree.Operations import Mathlib.RingTheory.PowerSeries.Binomial import Mathlib.Tactic.Ring
Formal statement
section
namespace D1Bound5
variable {F : Type*} [Field F] [CharZero F]
theorem _root_.D1Bound5.bennett_two_clear_column_two
(a b c : F) (ha : a ≠ 0) (hab : a ≠ b)
(k d0 d1 d2 h0 h1 h2 : ℕ) (hk : 1 ≤ k)
(hd : d0 + d1 + d2 = 1) (hh : h0 + h1 + h2 + 1 = k + d2) :
(a * b * (a - b) ^ 2) ^ k * (a * b * c + a) ^ (k - h2) *
(a⁻¹) ^ (k + d0 + h0) * ((a - b)⁻¹) ^ (k + d1 + h1) =
b ^ k * (b * c + 1) ^ (k - h2) * a ^ (d1 + h1) *
(a - b) ^ (k - (d1 + h1)) := by sorry
end D1Bound5
end
Source
D1Bound5/BennettTwoDenominatorClearing.lean, lines 74-101, SHA-256 21eca1644697a9c747a683cd3c26583cb9a60c7838c517047d556b782f76b0da. Project: https://github.com/tomislav-math/d1-bound5-lean