Theorems · Theorem · number theory

fermatLastTheoremWith_of_fermatLastTheoremWith_coprime

∀ {n : ℕ} {R : Type u_2} [inst : CommSemiring R] [IsDomain R] [inst_2 : DecidableEq R] [inst_3 : NormalizedGCDMonoid R],
  (∀ (a b c : R), a ≠ 0 → b ≠ 0 → c ≠ 0 → {a, b, c}.gcd id = 1 → a ^ n + b ^ n ≠ c ^ n) → FermatLastTheoremWith R n

To prove Fermat Last Theorem in any semiring that is a NormalizedGCDMonoid one can assume that the gcd of {a, b, c} is 1.

Defined in

Mathlib.NumberTheory.FLT.Basic

Cited by

0 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringIsDomainDecidableEqNormalizedGCDMonoid