Question 22
Let $(a_n)_{n \ge 0}$ be the sequence of rational numbers with $a_0 = 2016$ and
$$
a_{n+1} = a_n + \frac{2}{a_n}
$$
for all $n \ge 0$.
Show that this sequence does not contain the square of a rational number.
$$
a_{n+1} = a_n + \frac{2}{a_n}
$$
for all $n \ge 0$.
Show that this sequence does not contain the square of a rational number.