Question 136
Let $a_{0}$ be a positive integer and $a_{n+1} = \sqrt{a_{n}^{2} + 1}$, for all $n \geq 0$.
1) Prove that for all $a_{0}$ the sequence contains infinitely many integers and infinitely many irrational numbers.
2) Is there an $a_{0}$ for which $a_{2010}$ is an integer?
1) Prove that for all $a_{0}$ the sequence contains infinitely many integers and infinitely many irrational numbers.
2) Is there an $a_{0}$ for which $a_{2010}$ is an integer?