Math 310: Problem set 4

Instructions: This problem set is due Friday, February 3, 2006. Your goal is not only to give correct answers but to communicate your ideas well. Make sure you use good English,
  1. Let a1 = 4, a2 = 16, and an+1 = 3an + 4an-1, for n > 1. Prove that an = 4n for all integers n > 0.
  2. Let a1 = 1, a2 = 2, and an+1 = an + an-1, for n > 1. Prove that an >= (3/2)n-1 for all integers n > 0.
  3. Use Euclid's method (which we will discuss Wed, Feb 1) to compute gcd(210632, 423137).