Conjecture Fieldbook

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Beal's conjecture

Source placement record

Beal's conjecture: for all integral solutions to A x + B y = C z {\displaystyle A^{x}+B^{y}=C^{z}} {\displaystyle A^{x}+B^{y}=C^{z}} where x , y , z > 2 {\displaystyle x,y,z>2} {\displaystyle x,y,z>2}, all three numbers A , B , C {\displaystyle A,B,C} {\displaystyle A,B,C} must share some prime factor.

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Source status
Open
Field
Number theory · Diophantine equations
Record type
Revision-pinned source placement
Verification
Source-index reviewed
Source grade
secondary
Reviewed
2026-07-27T18:04:33.834Z

Context and review boundary

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Formal boundary

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Known approaches and partial results

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Source trail

  1. Wikipedia list subsection — Exact Number theory › Diophantine equations subsection in the revision-pinned source.
  2. Wikipedia topic article — Background article linked by the source index; follow its references for deeper study.
  3. Pinned source revision 1366281547 — Revision-pinned snapshot from 7/27/2026.