## 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.
- Find gcd(85, 75). You don't have to use Euclid's method,
but if you use some other method, justify your answer.
- Find integers m and n such that m85 + n75 = gcd(85, 75).
Show how you found m and n.
- Find two more different integer linear combinations of
85 and 75 which also equal gcd(85, 75).
- What is the least positive m that works?
Justify your answer.
- Find integers m and n such that m111 + n51 = gcd(111, 51).