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| Format: | Recurso digital |
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| Veröffentlicht: |
Zenodo
2025
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| Online-Zugang: | https://doi.org/10.5281/zenodo.17307971 |
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Inhaltsangabe:
- <p>This study explores the potential relationship between the Algebraic Structure<br>of Cyclic Cosets (LCC) in cyclic rings and Goldbach’s Conjecture. We<br>computationally verified that the LCC structure in ℤ63 acts as a perfect collector,<br>encompassing the entire set of prime numbers ℙ < 64. Based on this inclusion,<br>and by leveraging the LCC structure to effectively bound Jacobi Sums by<br>grouping Galois conjugate characters (Theorem 4.1), we prove that Goldbach’s<br>Conjecture is true for all even numbers > 0<br>. Quantitative calculation shows that 0 is reduced to a threshold of N0 ≈ 10^15, which falls within the<br>computationally verified range, comple</p>