Question 96
Let $a$ be a given integer. Prove that there exist infinitely many prime numbers $p$ such that
$$
p \mid n^2 + 3, \quad p \mid m^3 - a
$$
for some integers $n$ and $m$.
$$
p \mid n^2 + 3, \quad p \mid m^3 - a
$$
for some integers $n$ and $m$.