MATH/CSCI 4116 Cryptography Assignment 3 1. Find ‘(2007), ‘(2008), and ‘(b), where b is the integer obtained from the last four digits of your student number. 2. Find the smallest nonnegative integers x such that (a) 7x ? 8 (mod 5); (c) 5x ? 7 (mod 11). (b) 9x ? 6 (mod 7); 3. Using the fact that 10 ? 1 (mod 9), resp. 10 ? -1 (mod 11), prove the following divisibility rules for integers in decimal notation: (a) “Casting out nines”, i.e., an integer is divisible by 9 if and only if the sum of its digits is divisible by 9.