flt5_case2
Disprovedalgebradescentdirichletflt-n5graph-theorynumber-theoryproved
FLT-5 Case 2: If a^5+b^5=c^5 (integers), gcd(a,b)=1, and 5 divides c, then contradiction. This is the harder case of FLT-5, proved by Dirichlet (1825) using infinite descent: from 5|c one shows 5^4|(a+b), and the coprime factor structure forces a smaller FLT-5 solution, contradicting well-ordering.
Preamble
import Mathlib.Data.Int.Basic import Mathlib.Data.Int.GCD
Formal statement
theorem flt5_case2 (a b c : ℤ) (h_eq : a ^ 5 + b ^ 5 = c ^ 5) (h_cop : Int.gcd a b = 1) (h5c : (5 : ℤ) ∣ c) : False := by sorry