1. What is the set of integers congruent to -15 modulo 11 ? 2. Find all possible pairs of integers (x,y) such that x+yxy(mod5). 3. Show how you can calculate 3120mod13 without using a calculator. 4. Suppose that a UPC reads 78007131Q012, where Q represents a digit that can no longer be identified. How can we recover Q? 5. Encode the message "IT IS 2023 " using the encoding function f(x)=(5x 129) mod36 on the extended alphabet {A0,B1,C2,,Z25,026,1 27,228,,935}. 6. Express gcd(450,120) as a linear combination of 120 and 450 . Show each step in reaching the solution