A short remark on a connection between Goldbach’s conjecture and quadratic forms

Mladen V. Vassilev-Missana
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 32, 2026, Number 3, Pages 622–628
DOI: 10.7546/nntdm.2026.32.3.629-631
Full paper (PDF, 128 Kb)

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Authors and affiliations

Mladen V. Vassilev-Missana
5 V. Hugo Str., Sofia-1504, Bulgaria

Abstract

In the paper, a new version of the binary/strong Goldbach’s conjecture is considered and discussed. It is based on quadratic forms representation and on a new conjecture, that establishes equivalence.

Keywords

• Binary/strong Goldbach’s conjecture
• Composite number
• Prime number

2020 Mathematics Subject Classification

• 11A41
• 11E25
• 11P32

References

1. Sasikumar, K. (2023). A conjecture equivalent to the Goldbach conjecture, and some consequences. At Right Angles, 16, 56–58.
2. Vassilev, P., Vassilev-Missana, M., & Atanassov, K. (2005). On some new conjectures equivalent to the strong Goldbach’s conjecture. Proceedings of the Jangjeon Mathematical Society, 8(2), 123–131.
3. Vassilev, P., Vassilev-Missana, M., & Atanassov, K. (2006). Corrigendum to “On some new conjectures equivalent to the strong Goldbach’s conjecture”. Proceedings of the Jangjeon Mathematical Society, 9(2), 233.
4. Vassilev-Missana, M. (2005). Goldbach’s n-perfect numbers as a key for proving the Goldbach’s conjecture. Notes on Number Theory and Discrete Mathematics, 11(1), 20–22.
5. Wang, Y. (2002). The Goldbach Conjecture. World Scientific, Singapore..

Manuscript history

• Received: 20 October 2026
• Revised: 26 October 2026
• Accepted: 29 October 2026
• Online First: 31 October 2026

Copyright information

Ⓒ 2026 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).