Proof of Fermat Last Theorem based on successive presentations of pairs of odd numbers. Solution properties of equation x^a+y^a=z^b
| Main Author: | Shestopaloff, Yuri K. |
|---|---|
| Format: | info publication-preprint Journal |
| Terbitan: |
, 2022
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| Subjects: | |
| Online Access: |
https://zenodo.org/record/6345319 |
Daftar Isi:
- A simpler proof of Fermat Last Theorem (FLT), formulated by Fermat in 1637, is suggested. 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. All cases converge to one equation, which is studied using presentation of pairs of odd integers with a successively increasing presentation factor of 2^r. At each presentation level, the equation has no solution for a certain subset of pairs of odd integers. Using introduced measure of such "no solution" subsets, we sum up the corresponding measures across subsequent presentation levels, and prove that this sum corresponds to all possible pairs of odd integers. Based on this result, we eventually prove that FLT equation has no integer solution. The proposed approach also allowed to prove that equation x^n + y^n = z^k has no integer solution, except for one particular combination of parameters, when solution is uncertain. The proposed methods and ideas can be used for studying other problems in number theory.
- This version was updated to version 3, https://zenodo.org/record/6349220.This is an open version of the earlier paper uploaded on September 26, 2021 (doi.org/10.5281/zenodo.5528926), with addition of a detailed introduction, consideration of equation x^n+y^n=z^k, and some other editorial changes. Information about the author, the proof and its preliminary validation is at https://shes-yu.livejournal.com/328.html. So far, two people agreed with the proof. Contact info is on the first page.