Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Recurso digital |
| Sprache: | Englisch |
| Veröffentlicht: |
Zenodo
2026
|
| Schlagworte: | |
| Online-Zugang: | https://doi.org/10.5281/zenodo.19599355 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Inhaltsangabe:
- <div class="Y3BBE"><strong class="Yjhzub">Abstract:</strong></div> <div class="Y3BBE">This paper presents a novel approach to explaining the validity of Fermat's Last Theorem and Euler's sum of powers conjecture through the internal architecture of numbers. The author utilizes a fundamental arithmetic principle: any natural number raised to the power k (N^k) can be represented as a sum of N consecutive odd numbers.</div> <div class="Y3BBE">By analyzing these sequences, the paper demonstrates a critical distinction between the second power and all higher powers:</div> <ol class="IaGLZe VimKh"> <li class="dF3vjf"><span class="T286Pc">For squares (k=2), the sequences are nested and continuous, starting from 1, which allows for the existence of Pythagorean triples (A^2 + B^2 = C^2).</span></li> <li class="dF3vjf"><span class="T286Pc">For higher powers (k > 2), a "structural gap" emerges as the starting odd number of each sequence shifts forward at an accelerating rate, defined by the formula X = N^(k-1) - (N-1).</span></li> </ol> <div class="Y3BBE">The author argues that the impossibility of decomposing a power into the sum of only two others for k > 2 is caused by a divergence in "nominal weight" (density) of the odd numbers. Even if the quantity of numbers in a sum is correct, their collective arithmetic mass from the beginning of the series cannot match the density required for a target block of a higher order.</div> <div class="Y3BBE">Furthermore, this model provides an arithmetic justification for Euler's conjecture, suggesting that at least k summands are required to "stitch" the structural gap inherent in the k-th degree. This theoretical framework serves as a foundation for the author's practical discovery of parametric series for "quadruples" of cubes (A^3 = B^3 + C^3 + D^3).</div> <div class="Fsg96"> </div>