I'm rather new to much of the theory behind all of this so have mercy :)
I just finished reading Fermat's Last Theorem which is a fascinating book.
This introduced me to the Taniyama-Shimura conjecture and subsequent
theorem. I've noticed that there are algorithms based on Elliptic Curves.
The Taniyama Shimura theorem says that you can directly map each Elliptic
curve to it's Modular form.
Recently, a new theorem was proved that lets you solve Elliptic equations
easily with the Modular form - see
http://www.academicpress.com/inscight/07091999/grapha.htm for details.
So, based on all of this, would there be some way write a program that used
these details to factor faster?
G-Man
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