Question 50
Let $(a_n)_{n=1}^\infty$ be a sequence of integers with $a_1 = 1$, $a_2 = 2$ and
$$
a_{n+2} = a_{n+1}^2 + (n+2)a_{n+1} - a_n^2 - n a_n
$$
for all $n \ge 1$.
a) Show that there exist infinitely many prime numbers dividing at least one term of this sequence.
b) Find three different prime numbers not dividing any term of this sequence.
$$
a_{n+2} = a_{n+1}^2 + (n+2)a_{n+1} - a_n^2 - n a_n
$$
for all $n \ge 1$.
a) Show that there exist infinitely many prime numbers dividing at least one term of this sequence.
b) Find three different prime numbers not dividing any term of this sequence.