TITLE:
On Fermat Last Theorem: The New Efficient Expression of a Hypothetical Solution as a Function of Its Fermat Divisors
AUTHORS:
Prosper Kouadio Kimou
KEYWORDS:
Fermat’s Last Theorem, Fermat Divisors, Barlow’s Relations, Greatest Common Divisor
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.13 No.1,
February
15,
2023
ABSTRACT: Denote by a non-trivial
primitive solution of Fermat’s equation (p prime).We introduce, for the first
time, what we call Fermat principal divisors of the triple defined as follows. , and . We
show that it is possible to express a,b and c as function of the Fermat principal divisors. Denote by the set of possible non-trivial solutions of the Diophantine equation .
And, let (p prime). We prove that, in the first
case of Fermat’s theorem, one has
.
In
the second case of Fermat’s theorem, we show that
, ,.
Furthermore,
we have implemented a python program to calculate the Fermat divisors of
Pythagoreans triples. The results of this program, confirm the model used. We
now have an effective tool to directly process Diophantine equations and that
of Fermat.