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Ribenboim, P. (1993) Density Results on Families of Diophantine Equations with Finitely Many Solutions. L’Enseignement Mathématique, 39, 3-23.

has been cited by the following article:

• 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.