Number Theory


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.

Download: PDF

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

Unique-IP document downloads: 46 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus