All of Pythagoras's Friends
March, 2018
A lot of the reason I read a particular textbook has to do with its portability. I've got a lot of moving around to do over the course of the day. If I want to kill the commute time, reading has always been my go-to. Reading on the bus is kinda nice, but if you've got a text that's a little too large, it can be prohibitive. Not to mention the fact that you've got to carry it around all day. Fortunately, there are a plentitude of texts that fit right in your pocket! The one I picked off the shelf today is called Introduction to Elliptic Curves and Modular Forms, by a guy named Neal Koblitz. He's a cryptographer at the university of Washington, and an adjunct faculty member here at Waterloo.
I don't actually know any number theory, though. So
this book has been an adventure. I've had to brush up
on some definitions, sit and ponder a few things. The
first problem I worked out today had to do with
primitive Pythagorean triples, which is a 3-tuple of
intergers
form a triple so-described, and that all primitive
Pythagorean triples take this form. Showing that this
is formulation of
The reason we know all primitive triples are found this way is the most interesting part. The easiest way to see it is to draw a picture:
Re-paramaterizing from