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.
  1. Read Chapter 2ABCD of the text.
  2. Find [7]-118 (i.e., the multiplicative inverse of 7 in Z/18Z). Show how you obtain your answer.
  3. Explain why [8]-118 does not exist (i.e., why 8 has no multiplicative inverse in Z/18Z).
  4. Find the least nonnegative value of x such that 7x == 11 mod 18. Show how you obtain your answer.
  5. Prove that 8x == 11 mod 18 has no solution.
  6. Find all values of x from 0 to 17 for 8x == 2 mod 18. Show how you know you found them all.