Due date: Sep 18 Exercise 1. Use the extended Euclidean algorithm to find x,y E Z satisfying gcd(a, b) - ax + biy for each of the following pairs of integers. (Show all work except for the long divisions.) 1. a 324,b 23 2. a 987,b 343 3. a = 98, b = 24 4. a 1003, b 25 5. a 341,b 88 Exercise 2. Write the following integers as a product of primes in standard form. Recall that standard from means that when we write a > 1 as a = p 1 . .rn where pi is prime for all i e {1,... ,n), we also insist that pi