congruent math

Homework 5

1.      List five integers (including negatives) that are congruent to 89 modulo 13.

2.      Prove that if  is an odd positive integer, then .

3.      Exercise 26 on page 209 in the textbook: Which memory locations are assigned by the hashing function h (k) = k mod 101 to the records of insurance company customers with these Social Security numbers?

A.    104578690

B.     432222187

C.     372201919

D.    501338753

4.      Encrypt the message “ATTACKATDAWN” using the following encryption function:

5.      Convert  and  to both their hexadecimal and octal expansions.

6.      Convert  to decimal.

7.      Multiply  and  by working through each step of the multiplication algorithm.

8.      Use the modular exponentiation algorithm to find 11⁶⁴⁴ mod 645.