Proof of Fermat Last Theorem based on successive presentations of pairs of odd numbers
| Main Author: | Shestopaloff Yuri K. |
|---|---|
| Format: | info publication-preprint eJournal |
| Bahasa: | eng |
| Terbitan: |
, 2020
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| Subjects: | |
| Online Access: |
https://zenodo.org/record/3873629 |
Daftar Isi:
- A proof of Fermat Last Theorem (FLT) is proposed. FLT was formulated by Fermat in 1637, and proved by A. Wiles in 1995. Here, a simpler proof, mostly based on new concepts, is considered. The proposed approaches can be used for other problems in number theory. The initial equation x^n + y^n = z^n is considered not in natural, but in integer numbers. It is subdivided into four equations based on parity of terms and their powers. Then, each such equation is studied separately. The first equation is presented as a binomial expansion of its terms. The second one uses presentations of pairs of odd numbers with a successively increasing factor of 2^r. The third equation is equivalent to the second one with regard to absence of solution. The fourth equation uses presentation of pairs of odd numbers with a factor of four, and transformation to the second power. All four equations have no solution in integer numbers. Thus, the original FLT equation has no solution too.
- Versions 6, 7 explain why it is legitimate to associate the "no solution" fraction of one with the whole set of pairs of odd numbers (because we deal with deterministic objects). The proof uses little conventional number theory approaches. It can be understood, if one is familiar with the notion of limit and introductory theorems of number theory (included in the text). Please make sure that you view the latest Version 7 (file Shestopaloff_86V3_z2.pdf). Now, the older Version 4 is displayed by default.