Problem 3: (9 points) Solve the following questions. (i) Use the definition of big-O notation to prove or disprove that n! is 0(2). (ii) Prove that the sum of the squares of two odd integers cannot be the square of an integer. (iii) Let n be a positive integer. Compute gcd (2n +1, 3n+2) by using the Euclidean algorithm