MATH 1302 - Discrete Mathematics The purpose of this assignment is to assess your understanding of Division algorithm and modular arithmetic. Through this assignment, you will be able to demonstrate your knowledge and problem-solving skills in these areas. Tasks: This week you have learned about the concepts of Division algorithm and modular arithmetic. To demonstrate your understanding of these concepts, please answer the following questions. Please ensure that you do not use the same examples discussed in the textbooks and resources. 1. Choose a pair of two-digit numbers and find their greatest common divisor. Show the steps. 2. Choose any one modular arithmetic operation (addition modulo or multiplication modulo n X ) from the set of positive integers (for example, 5= {0,1,2,3,4} do not use the same example with your choice of n. Find the identities and inverses of all elements with respect to the operation you choose. If they do not exist, explain why. You can use an operation table to explain your reasoning. (The table can be drawn using MS Word.) 3. Find and explain solution for the equation x2+ 5x +1 = 0 in 3, the integers modulo 3