## An Identity-Based Direct Proof of FLT V7

**Authors:** Philip Aaron Bloom

By inspection, for some positive integral n (e.g., n=1,2) there clearly exist positive integers A, B, C satisfying A^n+B^n = C^n, an algebraic identity that we have devised with one unrestricted real variable. We find a way around the circularity inherent to this identity, allowing us to show that the positive coprime triple (A,B,C) is equal to the positive coprime triple (x,y,z) that satisfies x^n+y^n=z^n. Our identity discloses, for n greater or equal to three, that no value of coprime (A,B,C) satisfies A^n+B^n=C^n. So, we prove FLT directly.

**Comments:** 2 Pages.

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### Submission history

[v1] 2018-01-17 20:03:01 (removed)

[v2] 2018-01-18 09:49:18 (removed)

[v3] 2018-01-22 19:52:33 (removed)

[v4] 2018-01-28 16:39:53 (removed)

[v5] 2018-01-31 18:48:53 (removed)

[v6] 2018-02-03 19:47:14

[v7] 2018-02-05 22:50:25

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