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
N^{x} + N^{y} = N^{z}
has no solutions in positive integers for N
greater than 2.
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 its 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."
Math Fun Facts.
<http://www.math.hmc.edu/funfacts>.
