Question 69
Let $S$ be an infinite set of positive integers, define:
$$
T = \{x + y \mid x, y \in S, x \neq y\}.
$$
Suppose that there are only finitely many primes $p$ such that:
a) $p \equiv 1 \pmod 4$.
b) There exists a positive integer $s$ such that $p \mid s$, $s \in T$.
Prove that there are infinitely many primes that divide at least one element of $S$.
$$
T = \{x + y \mid x, y \in S, x \neq y\}.
$$
Suppose that there are only finitely many primes $p$ such that:
a) $p \equiv 1 \pmod 4$.
b) There exists a positive integer $s$ such that $p \mid s$, $s \in T$.
Prove that there are infinitely many primes that divide at least one element of $S$.