 
Summary: A MILLIONDOLLAR PROOF
AARON ABRAMS
I came up with the main theorem of this paper during the summer of 1992 while I
was an undergraduate student at Joe Gallian's REU at the University of Minnesota,
Duluth. Until recently, I neither shared it with anyone nor fully appreciated its
value. But now Fermat's Last Theorem has a proof, and it seems like the PoincarŽe
Conjecture does too, and with ever more attention directed toward problems like
these, I thought I'd better get this in print.
Here is the theorem:
Theorem 1. N = 1.
The proof is based on what I thought at the time was a surprising observation,
namely the following identity:
(1)
N=0
1
2N
=
N=0
