The Cartesian method and Fermat's Last Theorem

Abstract: Fermat's Last Theorem is proved by using the philosophical and mathematical knowledge of 1637 when the French mathematician Pierre de Fermat claimed to have a truly marvelous proof of his conjecture. Our approach consists of setting three variables of Fermat's equation as integers and then evaluating whether the remaining variable can be an integer as well. Pythagorean triples play a fundamental role in claiming that at least an irrational number is needed to satisfy Fermat's equation. As a result, we confirm that Fermat's Last Theorem is valid.