## Beal’s Conjecture as Sum of Two Vectors in Polynomial Vector Space that Defines One-Variable Polynomial Identity-Proof

**Authors:** Kamal Barghout

Beal’s equation is identified as polynomial identity. The central theme to prove Beal’s conjecture here is identifying its numerical solution as a specific solution to the polynomial identity of αx^l+βx^l=〖δx〗^l, where α,β, δ, and l are positive integers and x is the indeterminate. Beal’s equation then may be represented by the sum of two same degree monomials representing two vectors in the vector space of polynomials in one variable with basis 1,x,x^2,x^3,x^4… and coefficients in Z of values zeros except for those of the two monomials. Accordingly, all three monomials of Beal’s equation numerically produce terms of single power by following the rules of exponentiation considering vector space operations: addition of polynomials, and multiplication by integer scalars.

**Comments:** 8 Pages. The material in this article is copyrighted. Please obtain authorization from the author before use of any part of the manuscript

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### Submission history

[v1] 2017-12-05 15:21:45 (removed)

[v2] 2017-12-07 09:57:31 (removed)

[v3] 2017-12-09 13:15:45 (removed)

[v4] 2017-12-12 13:11:08 (removed)

[v5] 2017-12-14 14:10:38 (removed)

[v6] 2017-12-18 06:46:20 (removed)

[v7] 2017-12-30 12:15:53

[v8] 2018-02-05 10:31:56

[v9] 2018-02-20 11:06:15

[vA] 2018-03-13 05:47:37

[vB] 2018-03-17 17:04:34

[vC] 2018-03-27 08:29:08

[vD] 2018-04-05 12:04:09

[vE] 2018-04-10 08:51:25

[vF] 2018-06-27 17:36:27

[vG] 2018-07-14 16:35:00

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