Number Theory

    

On Goldbach’s Conjecture: An Algebraic and Combinatorial Formulation

Authors: Mar Detic

We present an algebraic and combinatorial formulation of Goldbach-type representations of integers as sums of primes. Every odd prime is written in the canonical linear form 2a + 1 (with a ∈ N0) and the sum of k primes becomes a linear Diophantine constraint on the corresponding a-variables. This transforms the problem into the study of integer lattice points on hyperplanes of the form Pk i=1 ai = N −k2 , together with primality filters on the linear forms 2ai + 1. We relate this combinatorial perspective to classical analytic heuristics (Hardy—Littlewood), additive-combinatorics sumset language, and partition/stars-and-bars counting, and we provide illustrative examples and an inline visualization for the k = 2 case.

Comments: 5 Pages.

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Submission history

[v1] 2021-05-17 19:21:55
[v2] 2021-05-24 09:25:13
[v3] 2025-06-21 21:32:03
[v4] 2025-10-14 20:34:16

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