tamreF's Last Theorem

Here's an amusing theorem that is very easy to prove, which we'll call tamreF's Last Theorem. In fact it is tamreF's only known theorem. It says:

The following equation

This theorem has not been unsolved for centuries; in fact, it was solved as soon as it was posed. It is much easier to prove than it's counterpart: Fermat's Last Theorem.

The Math Behind the Fact:
The proof is ridiculously easy; consider the equation in base N. Perfect powers of N consist of a 1 followed by many zeroes. Adding two such numbers cannot be a number of that form unless N=2 and the 1's are in the same position.

How to Cite this Page:
Su, Francis E., et al. "tamreF's Last Theorem." Mudd Math Fun Facts. <http://www.math.hmc.edu/funfacts>.

References: I have been told that the reference is in a Martin Gardner book, but I don't have the reference! Keywords:    Fermat's last theorem Subjects:    number theory Level:    Easy Fun Fact suggested by:   Arthur Benjamin Suggestions? Use this form. 3.56 current rating Click to rate this Fun Fact...     *   Awesome! I totally dig it!     *   Fun enough to tell a friend!     *   Mildly interesting     *   Not really noteworthy and see the most popular Facts!

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