SOME CASES OF THE LAST FERMAT THEOREM
Arithmetic. Fermat's equation. Sophie Germain. Pythagoras.
Mathematics is one of the most exact sciences, but that time and again it becomes a
box of surprises. One such situation is the amount of new theories that were needed to
answer a problem known in the literature as Fermat's Last Theorem, which is apparently
so simple because it is composed only of basic operations - such as sum and multiplication
- and challenged great mathematicians for 358 years. In this work, results that prove the
validity of some special cases, such as when n is a multiple of 4, have been presented
with the intention of being an introduction. Historically, the importance of solving this
problem is not only the result itself, but the substantial gain of properties and theories
that was obtained by mathematicians in the search for such a solution. It is written, for
the most part, under the basic properties of Mathematics so that students interested in
the subject can understand it, with a little more study than the one referring to Regular
High School. Like Andrew Wiles, at age ten, one day he found in a library a book of
mathematical puzzles in which one of them became his life goal. We hope this work will
inspire young students to have this kind of problem as a good hobby.