The Beal Conjecture and the Modulus

The Beal Conjecture states: if Aˣ + Bʸ = Cᶻ where A, B, C, x, y, zare positive integers and x, y, z ≥ 3, then A, B, and C have acommon prime factor. This paper establishes the Beal Conjecture within the Prime FieldArchitecture — a self-contained arithmetic framework built on themodulus M = 30 = 2 × 3 × 5. The paper requires no prior knowledge ofthe Prime Field Architecture; all necessary definitions are providedhere.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-06
DOI
https://doi.org/10.5281/zenodo.24027685
Primary Topic
Algebraic Geometry and Number Theory
Type
preprint
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preprint

The Beal Conjecture and the Modulus

David-Michael Skerl
Zenodo (CERN European Organization for Nuclear Research)
Algebraic Geometry and Number Theory
preprint

The Beal Conjecture and the Modulus

David-Michael Skerl
preprint en

Abstract

The Beal Conjecture states: if Aˣ + Bʸ = Cᶻ where A, B, C, x, y, zare positive integers and x, y, z ≥ 3, then A, B, and C have acommon prime factor. This paper establishes the Beal Conjecture within the Prime FieldArchitecture — a self-contained arithmetic framework built on themodulus M = 30 = 2 × 3 × 5. The paper requires no prior knowledge ofthe Prime Field Architecture; all necessary definitions are providedhere.

Zenodo (CERN European Organization for Nuclear Research)
Algebraic Geometry and Number Theory
DOIOpen Access PDFOpenAlex
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The Beal Conjecture and the Modulus — David-Michael Skerl · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS