Number Theory


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

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Submission history

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

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