Homework 2
Math 108, Spring 2015
Due Date: Friday, February 13
Instructions: Feel free to work together with other students in the class, though you must
turn in your own copy of the solutions, and you must acknowledge anyone that you worked
with. You can turn in your homework assignment by e-mailing me your Excel workbook
(belk@bard.edu), which should include your worksheet for question 2 as well as whatever
work you did for question 3. You can include the answers to question 1 in either your e-mail
or in your Excel file.
1. Solve the following problems by hand.
(a) Compute 7 + 8 mod 9.
(b) Compute 5 × 10 mod 13.
(c) Find the inverse of 3 modulo 7.
2. The following table shows multiplication by 7 mod 10.
0 1 2 3 4 5 6 7 8 9
0 7 4 1 8 5 2 9 6 3
(a) Use Excel to make a similar table for multiplication by 7 mod 37. The first row
of your spreadsheet should have the numbers 0 through 36, and the second row
should show the results of multiplying these numbers by 7 mod 37.
(b) Based on your table, what is the inverse of 7 modulo 37?
3. The following text was encrypted using a decimation cipher. Decipher the message.
W Y C C Y N Q S N Q S K Q N Y B Q Y W Y C C Y N
(I would recommend using Excel for this problem.)