## Revisit of Carmichael 1913 Work and an Elementary Approach for Fermat’s Last Theorem of Case I

**Authors:** Gang Li

We discuss an elementary approach to prove the first case of Fermat's last theorem (FLT). The essence of the proof is to notice that
$a+b+c$ is of order $N^{\alpha}$ if $a^N+b^N+c^N=0$. To prove FLT, we first show that $\alpha$ can not be $2$; we
then show that $\alpha$ can not be $3$, etc. While this is is the standard method of induction, we refer to it here as
the ``infinite ascent'' technique, in contrast to Fermat's original ``infinite descent'' technique. A conjecture, first noted by Ribenboim is used.

**Comments:** 13 Pages. Submitted to JNT. This is an improved version of the paper posted at http://vixra.org/abs/1706.0288

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### Submission history

[v1] 2018-05-09 19:09:09

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