## 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.
- x
^{2} = 17 (mod 23)
- x
^{2} = 6 (mod 23)
- x
^{2} = 32927 (mod 47407)
- x
^{2} = 14480 (mod 47407)
- x
^{2} + 6x + 3 = 0 (mod 23)
- x
^{2} + 22222x + 20973 = 0 (mod 47407)