MathDB

Let

S

be an infinite set of positive integers and define:

T=\{ x+y|x,y \in S , x \neq y \}

Suppose that there are only finite primes

p

so that:
1.

p \equiv 1 \pmod 4

2.There exists a positive integer

s

so that

p|s,s \in T

.
Prove that there are infinity many primes that divide at least one term of

S

Problem Statement