### An Application of Fermat's Last Theorem

**Theorem**

The following proof has been submitted by Richard Ehrenborg, University of North Carolina, Charlotte and published in the *American Mathematical Monthly* (May 2003, 423) with a remark that the proof was found by William Henry Schultz, at the time an undergraduate at UNC-Charlotte.

The proof has been reproduced in a recent book from MAA (C. Alsina, R. B. Nelsen, *Charming Proofs*, p. 36.)

Curiously, the proof relies on *Fermat's Last Theorem*. Not that the theorem was lacking in elementary proofs, but using the FLT made it into an elegant math joke.

**Proof**

Assuming that is rational: where both and are positive integers. Rewrite this identity as Now by a result of Andrew Wiles, we know that there are no such and

If Fermat's Last Theorem has no practical application, then what good is it?

May 25th, 2015 at 4:52 pmYou may want to read

https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

by a Nobel Prize winner Eugene Wigner.

May 26th, 2015 at 10:58 am