## 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,
- Let a
_{1} = 4, a_{2} = 16,
and a_{n+1} = 3a_{n} + 4a_{n-1},
for n > 1. Prove that a_{n} = 4^{n} for all
integers n > 0.
- Let a
_{1} = 1, a_{2} = 2,
and a_{n+1} = a_{n} + a_{n-1},
for n > 1. Prove that a_{n} >= (3/2)^{n-1} for all
integers n > 0.
- Use Euclid's method (which we will discuss Wed, Feb 1)
to compute gcd(210632, 423137).