Algebraic Method for Goldbach's Conjecture: Application of the Cyclic Coset Structure (LCC)
Year: 2025
Type: article
Abstract: This study explores the potential relationship between the Algebraic Structureof Cyclic Cosets (LCC) in cyclic rings and Goldbach’s Conjecture. Wecomputationally verified that the LCC structure in ℤ63 acts as a perfect collector,encompassing the entire set of prime numbers ℙ < 64. Based on this inclusion,and by leveraging the LCC structure to effectively bound Jacobi Sums bygrouping Galois conjugate characters (Theorem 4.1), we prove that Goldbach’sConjecture is true for all even numbers 𝑁 > 𝑁0. Quantitative calculation shows that 𝑁0 is reduced to a threshold of N0 ≈ 10^15, which falls within thecomputationally verified range, comple
Author: VU TAT THANH
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7086976979
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