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2025
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| Online Access: | https://doi.org/10.5281/zenodo.17307971 |
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| _version_ | 1866901784849547264 |
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| author | VU TAT THANH |
| author_facet | VU TAT THANH |
| contents | <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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17307971 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Algebraic Method for Goldbach's Conjecture: Application of the Cyclic Coset Structure (LCC) VU TAT THANH <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> |
| title | Algebraic Method for Goldbach's Conjecture: Application of the Cyclic Coset Structure (LCC) |
| url | https://doi.org/10.5281/zenodo.17307971 |