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
Nx + Ny = Nz
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. <https://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!
Fun Fact suggested by:
Arthur Benjamin