**Authors:** Philip A. Bloom

A simple proof of Fermat's last theorem (FLT) for each integral n > 2 is not confirmed. Our simple proof of FLT is based on our algebraic identity, denoted (for convenience) as r ^ n + s ^ n = t ^ n. For positive integral n, we relate ( r, s ,t ), a function of two variables, for which r ^ n + s ^ n = t ^ n holds, with ( x, y, z ) for which x ^ n + y ^ n = z ^ n holds. We infer by direct argument ( not by way of contradiction ), for any given n, 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 } . In addition, we show, for n > 2, that {( r, s, t ) | r, s, t in Z, r ^ n + s ^ n = t ^ n } is null. Thus, for values of n > 2, it is true that { ( x, y, z ) | x, y, z in Z, x ^ n + y ^ n = z ^ n } is null.

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[v1] 2018-05-22 15:54:17

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[v8] 2018-08-07 11:31:29

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[vA] 2018-08-18 13:16:39

[vB] 2018-08-21 09:29:28

[vC] 2018-08-24 16:55:01

[vD] 2018-08-31 18:52:05

[vE] 2018-09-18 09:44:53

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