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The Wonders of Arithmetic from Pierre Simon de Fermat
The Wonders of Arithmetic from Pierre Simon de Fermat
Abstract
Within the framework of the designated topic:
1. There are restored some little-known facts from the Pierre Fermat's biography.
2. For the first time, there are given two definitions (mathematical and general) the concept of number, as well as a new versions axioms and basic properties of numbers following from them.
3. There is shown fallacy of Euclid, Gauss, and Zermelo's proofs of the Basic Theorem of Arithmetic (BTA), without which the foundation of the whole science collapses.
4. There are given comments on Zermelo's proof of the Basic Theorem of Arithmetic.
5. There is restored the Fermat’s BTA proof by the descent method.
6. There is restored a simplest method of proving the FLT for the 4th power.
7. There is shown the fallacy of the G. Frey’s idea lied in the basis of the A. Wiles’ FLT proof 1995.
8. There is restored the Fermat’s proof of his Last Theorem on the basis of a new way to solving the Pythagoras’ equation x2+y2=z2 by using the formula, discovered by him and called Fermat Binomial.
9. As a consequence of the FLT proof there are formulated Theorems on Magic Numbers, the validity of which is confirmed by examples of calculations.