You may turn these problems in electronically to the drop boxes or on paper. If you do your problems electronically, please use a proper equation editor rather than trying to fake the mathematical symbols!

Drop box submissions are due at midnight on the due date. Paper submissions are due in class or in the box outside my office by 5:00 p.m.

Show your work on all problems.

I will give some partial credit, especially on multi-part problems.

 

1. [1 point.] Use Fermat's Little Theorem to find a number a between 0 and 72 with a congruent to 9794 modulo 73.
    
2. [2 points.] Use Fermat's Little Theorem to find a number x between 0 and 28 with x85  congruent to 6 modulo 29.  (You should not need to use any brute force searching!)
    
3. [2 points.]  Use Euler's Formula to find a number a between 0 and 9 such that a is congruent to 71000 modulo 10.  (Note that this is the same as the last digit of the decimal expansion of  71000.)
    
4. [4 points.] Use Euler's Formula to find a number x between 0 and 28 with x85  congruent to 6 modulo 35.  (You should not need to use any brute force searching!)
   
   The following problems are from your textbook.
    
5. [6 points.] Problem 8.1.
6. [4 points.] Problem 9.1.
7. [2 points.] Problem 9.2(a and e). Do not use Maple, but do use any tricks you can.
8. [1 point.] Problem 9.3.
9. [1 point.] Problem 9.4.
10. [2 points.] Problem 9.6.
11. [10 points.] Problem 9.7. 1 point for a yes or no answer. (Up to) 9 more points for a detailed explanation of how to crack the new key.
12. [4 points.] Problem 9.8.
13. [2 point.] Problem 9.9.
14. [4 points.] Problem 9.10.