Assignment 2
6104: Algorithmic Number Theory
Each problem in this assignment is worth 50 points.
The assignment is due by 9:30AM on June 1, 1998.
Prepare your solutions in LaTeX,
preferably using this file as a starting point.
You may submit your solutions in printed form
or
by email to cs6104@ei.cs.vt.edu.
Explain your solution to each problem,
including references to the appropriate theorems
in the textbook.
Help is available by email as well as during my office hours.
It is especially helpful to request clarification or hints by email
to cs6104@ei.cs.vt.edu,
so I can send the response to everyone.
The person assigned to present the solution to a problem (if anyone) is noted at the beginning of the problem.
Chapter 4, Problem 14. You may assume the result in Problem 2.22. Use Mathematica to calculate the actual probability for
Put those results in a table
that also gives the relative error
if the probability is taken to be 
.
Implement the Extended Euclidean algorithm in Mathematica. (Mathematica has the Euclidean and Extended Euclidean algorithms built in, but do not use those in your implementation.)
Let
Show how your implementation can be used to find
a solution 
to the equation
Give the Mathematica steps to obtain one such solution.