My Supervisor wants me to give a talk on part of my project, and decided that the Nagell-Lutz theorem was the most interesting, yet easiest to convey, piece of reading I had done.
The problem is, I know that the theorem isn't an "iff" statement - having
(where D is the discriminant of f(x)), does not mean that
is a point of finite order. Alas, I'm having trouble finding such a point.
I want to use the curve
, and I thought that the point
would be a good candidate (as it satisfies all of the conditions of the converse of the theorem). However, trying to calculate 2P I keep getting
, which is not on the curve (
). I can't work out what I'm doing wrong - the formulae I'm using is correct because I've used it plenty of other times to duplicate points, and once I work out the kinks with this stupid point, it will clearly be contradiction to the converse (as P will satisfy all of the conditions, but have infinite order). So can someone tell me where I'm going wrong? Because this is starting to irritate me.
The formulae I'm using are:
"It's never crowded along the extra mile"
Graduated, and done with maths forever