Question 4
Let $(a_n)_{n \ge 1}$ be a sequence given by $a_1 = 45$ and
$$
a_n = a_{n-1}^2 + 15a_{n-1}
$$
for $n \gt 1$. Prove that the sequence contains no perfect squares.
$$
a_n = a_{n-1}^2 + 15a_{n-1}
$$
for $n \gt 1$. Prove that the sequence contains no perfect squares.