Math 310: Problem set 10

Instructions: This problem set is due Friday, March 31, 2006. Explain each of your steps. However, you may use results from the web site http://www.math.unl.edu/~bharbourne1/M310Spr06/extras/powersmodm.html, if you find it useful for doing calculations.

For each problem below, find all least positive residues which are solutions or explain why there is no solution.
  1. x2 = 17 (mod 23)
  2. x2 = 6 (mod 23)
  3. x2 = 32927 (mod 47407)
  4. x2 = 14480 (mod 47407)
  5. x2 + 6x + 3 = 0 (mod 23)
  6. x2 + 22222x + 20973 = 0 (mod 47407)