Number Theory


A Simple, Direct Proof, Using Set-Theory, of Fermat's Last Theorem (FLT)

Authors: Philip A. Bloom

There is no confirmed, simple proof of Fermat's last theorem (FLT) for each integral n > 2. Our proposed, simple proof of FLT is based on our algebraic identity, a function of two variables, denoted for convenience as r ^ n + s ^ n = t ^ n. For positive integral values of n, we relate ( r, s ,t ) for which r ^ n + s ^ n = t ^ n holds, with ( x, y, z ) for which x ^ n + y ^ n = z ^ n holds. From these true equations we infer by direct argument ( not by way of contradiction ), that { ( r, s, t ) | r, s, t in Z, r ^ n + s ^ n = t ^ n } = { ( x, y, z )| r, s, t in Z, x ^ n + y ^ n = z ^ n } for any given n for which these sets are nonempty. Also, we show, for n > 2, that {( r, s, t ) | r, s, t in Z } is null. Hence, for n > 2, set { ( x, y, z ) | x, y, z in Z } is null

Comments: 3 Pages.

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Submission history

[v1] 2018-05-22 15:54:17
[v2] 2018-05-24 23:48:32
[v3] 2018-05-30 11:22:41
[v4] 2018-06-05 13:36:54
[v5] 2018-06-29 23:35:11
[v6] 2018-07-09 21:33:43

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