Math 310: Problem set 5

Instructions: This problem set is due Friday, February 10, 2006. On this problem set, except for Problem 4, it is enough to show the steps of your calculations.
  1. Find gcd(85, 75). You don't have to use Euclid's method, but if you use some other method, justify your answer.
  2. Find integers m and n such that m85 + n75 = gcd(85, 75). Show how you found m and n.
  3. Find two more different integer linear combinations of 85 and 75 which also equal gcd(85, 75).
  4. What is the least positive m that works? Justify your answer.
  5. Find integers m and n such that m111 + n51 = gcd(111, 51).