Number Theory


A Short Proof of Fermat's Last Theorem

Authors: Morgan D. Rosenberg

Presented herein is a proof of Fermat's Last Theorem, which is not only short (relative to Wiles' 109 page proof), but is also performed using relatively elementary mathematics. Particularly, the binomial theorem is utilized, which was known in the time of Fermat (as opposed to the elliptic curves of Wiles' proof, which belong to modern mathematics). Using the common integer expression an + bn = cn for Fermat's Last Theorem, the substitutions c = b+i and b = a+j are made, where i and j are integers. Using a Taylor expansion (i.e., in the form of the binomial theorem), Fermat's Last Theorem reduces to (see paper) and what remains to be proven, from this equation, is that (see paper) only has rational solutions for n=1 and n=2. This proof is presented herein, thus proving that an + bn = cn only has integer solutions for a, b and c for integer values of the exponent n=1 or n=2.

Comments: 11 pages

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Submission history

[v1] 8 Aug 2010
[v2] 29 Nov 2011

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