Question 4
Consider the sequence $(a_n)_{n=1}^\infty$ defined as follows:
$$
a_1 = 3 \quad a_n = a_1a_2a_3 \dots a_{n-1} - 1 \quad \text{for all } n \ge 2.
$$
*Prove that there exist*
a) infinitely many primes dividing at least one member of this sequence;
b) infinitely many primes dividing no member of this sequence.
$$
a_1 = 3 \quad a_n = a_1a_2a_3 \dots a_{n-1} - 1 \quad \text{for all } n \ge 2.
$$
*Prove that there exist*
a) infinitely many primes dividing at least one member of this sequence;
b) infinitely many primes dividing no member of this sequence.