Classical Algebra Written Assignment No. 1

due Friday, February 16, 2001

Obtain a computer account on the campus network. Write a Maple program^{1} for finding the sequence of quotients and remainders arising from application of the Euclidean algorithm to an ordered pair (x, y) of positive integers x and y. Write a paragraph or two explaining how to use your program. Use your program to find the continued fraction expansions of the following rational numbers:

1. 360/1728.

2. 987654321/123456789.

3. 13^{11}/11^{13}.

By email send:

• a listing of the source code for your program

• the directions for using your program

• the answers to the three exercises that you obtained using your program

to hammond@math.albany.edu.

1You may use another computer language with arbitrary precision integer arithmetic if you know one and if the language is available to users logged into the network at csc.albany.edu.