MTH 337 Homework #1 due 5pm Thursday, Jan 31

1. Finish writing, as a plain text file, your Maple procedure 
mygcd(a,b) that returns the greatest common divisor of the positive 
integers a and b. Put this file in the Digital Drop Box. 

2. 
(a) The code http://orange.math.buffalo.edu/337/pythag_triples.maple, 
generates (in a very brute-force way) all Pythagorean triples [a,b,c] 
up to a certain size. Modify this code so that it only generates all 
*primitive* Pythagorean triples, using your "mygcd" function.

(b) Generate all the primitive triples with "c" up to 400.
(Check: You should find 16 of them with "c" up to 100.)
Put your Maple code in plain text format in the Digital Drop Box.

(c) Make a 2D point plot that shows the [a,b]'s of all the
triples you've generated. Create an EPS file of this plot.

(d) Study the list of triples and the plot, and write down one
thing that interests you about this collection of objects.

3. Using OpenOffice, briefly write up what you have done and observed
in 1 and 2. Include in your document the Maple codes and the results, 
including the plot. Drop your odt file in the Digital Drop Box.