Fermat and Pythagoras Divisors for a New Explicit Proof of Fermat’s Theorem:a⁴ + b⁴ = c⁴. Part I

In this paper we prove in a new way, the well known result, that Fermat’s equation a⁴ + b⁴ = c⁴, is not solvable in $\mathbb{N}$ , when $abc\ne 0$ . To show this result, it suffices to prove that: $\left(F_0\right):a_1^4+{\left(2^s{b}_1\right)}^4=c_1^4$ , is not solvable in $\mathbb{N}$ , (where $a_1\mathrm{,}{b}_1\mathrm{,}{c}_1\in 2\mathbb{N}+1$ , pairwise primes, with necessarly