## Math 310: Problem set 2

*Instructions*: This problem set is due
Thursday, September 7, 2006.
Your goal is not only
to give correct answers but to communicate
your ideas well. Make sure you use good English.
- Read Chapter 2ABCD of the text.
- Find [7]
^{-1}_{18} (i.e., the multiplicative
inverse of 7 in **Z**/18**Z**). Show how you obtain your answer.
- Explain why [8]
^{-1}_{18} does not exist
(i.e., why 8 has no multiplicative
inverse in **Z**/18**Z**).
- Find the least nonnegative value of x
such that 7x == 11 mod 18. Show how you obtain your answer.
- Prove that 8x == 11 mod 18 has no solution.
- Find all values of x from 0 to 17
for 8x == 2 mod 18. Show how you know
you found them all.