M417 Homework 1 Spring 2004

Instructions: Be prepared to discuss and present in class on Wed., January 21. Written solutions are due Fri., January 23.

  1. #4, p. 23
  2. #5, p. 23
  3. Let a and b be positive integers. Let g = gcd(a, b), and let a'=a/g and b'=b/g. For each of the following statements, if it is false, give a counterexample; otherwise give a proof.
  4. Let a and b be positive integers. Let g = gcd(a, b), m = lcm(a, b), and let a' = a/g and b' = b/g and define a'' and b'' such that m = aa'' = bb''.
  5. Using the error correcting ``circle'' code discussed in class, determine the correct message encoded by the following code words: 1010101, 1101011, 1100101, 1100011, 1111111.