**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
a^{n} + b^{n} = c^{n} 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
a^{n} + b^{n} = c^{n} only has
integer solutions for a, b and c for integer values of the exponent n=1 or n=2.

**Comments:** 11 pages

**Download:** **PDF**

[v1] 8 Aug 2010

[v2] 29 Nov 2011

**Unique-IP document downloads:** 659 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful. *