Question 40
We consider the sequences $(a_n)_{n \ge 0}$ and $(b_n)_{n \ge 0}$ which are defined by $a_0 = b_0 = 2$ and $a_1 = b_1 = 14$ and by
$$
a_n = 14a_{n-1} + a_{n-2},
$$
$$
b_n = 6b_{n-1} - b_{n-2}
$$
for $n \ge 2$.
Decide whether there are infinitely many integers which occur in both sequences.
$$
a_n = 14a_{n-1} + a_{n-2},
$$
$$
b_n = 6b_{n-1} - b_{n-2}
$$
for $n \ge 2$.
Decide whether there are infinitely many integers which occur in both sequences.