TITLE:
New Asymptotic Results on Fermat-Wiles Theorem
AUTHORS:
Kimou Kouadio Prosper, Kouakou Kouassi Vincent, Tanoé François
KEYWORDS:
Fermat’s Last Theorem, Fermat-Wiles Theorem, Kimou’s Divisors, Diophantine Quotient, Diophantine Remainders, Balzano Weierstrass Analysis Theorem
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.14 No.6,
June
4,
2024
ABSTRACT: We analyse the Diophantine equation of Fermat xp yp = zp with p > 2 a prime, x, y, z positive nonzero integers. We consider the hypothetical solution (a, b, c) of previous equation. We use Fermat main divisors, Diophantine remainders of (a, b, c), an asymptotic approach based on Balzano Weierstrass Analysis Theorem as tools. We construct convergent infinite sequences and establish asymptotic results including the following surprising one. If z – y = 1 then there exists a tight bound N such that, for all prime exponents p > N , we have xp yp ≠ zp.