Question 79
For a positive integer $a$, let $S_a$ be the set of primes satisfying the following condition:
(condition) For any $p \in S_a$, there exists an odd integer $b$ such that $(2^{2^a})^b - 1$ is divisible by $p$.
For any positive integer $a$, prove that there exist infinitely many primes that are not contained in $S_a$.
(condition) For any $p \in S_a$, there exists an odd integer $b$ such that $(2^{2^a})^b - 1$ is divisible by $p$.
For any positive integer $a$, prove that there exist infinitely many primes that are not contained in $S_a$.