1. (8 marks) Suppose that bo, bi, b2,... is a sequence defined as follows: bo 1, b 2, b2 3, and bk-bk-1 4bk-2 +5bk-3 for all integers k2 3. Prove by mathematical induction that bn 3" for all integers n 2 0. 2. (8 marks) Prove the existence part of the unique factorization of integers theorem, that is: Every integer greater than 1 is either prime or a product of prime numbers. Use mathematical induction or the well-ordering principle