Math 310: Problem set 9

Instructions: This problem set is due Friday, March 10, 2006.
  1. Let a and b be integers, and let m and n be positive integers. Consider the problem:
    x = a mod m
    x = b mod n
  2. (2 points) Find all integer solutions x which are simultaneously congruent to 17 mod 105 and to 5 mod 99. Explain how you find them.
  3. Find a solution to each of the following problems, or explain why there is no solution.