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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.
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David-Michael Skerl (2026) studied this question.
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