Abstract is aⁿ+ bⁿ = cⁿ? , a gt b gt c, & a, b, c, n ϵN_+, ngt 2 ⇔ Fermat' s Last Theorem ∎Taha’s Coefficient Fact1 (TCF1): a+b =c ⇒ aa^ (r-1) +bb^ (r-1) ≠cc^ (r-1) ⇒aʳ+bʳ≠cʳ, when aʳ≠bʳ≠cʳ, r≠1, r ϵN_+. ∎Taha’s Coefficient Fact2 (TCF2): a+b ≠ c ⇒ aa^ (r-1) + bb^ (r-1) ≠cc^ (r-1) ⇒aʳ+bʳ ≠ cʳ, when aʳ≠bʳ≠cʳ, r≠1, r ϵN_+.
Taha Muhammad (Mon,) studied this question.