I am revising for a number theory exam and have a question that I am struggling with, any help would be greatly appreciated.
First I am asked to show that for an odd number $x$, $x^2+2 ≡3$(mod 4).
I can do this part of the question, but next I am asked to deduce that there exists a prime $p$ where $p$ divides $x^2 +2$ and $p≡3$ (mod 4)
I am struggling to see how to attempt the second part and how the first part relates.
My thoughts so far are that I want to show $x^2≡-2$(mod p) ? And perhaps Fermat's Little Theorem could be of use here somehow?
Not sure if I'm barking up the wrong tree though.
Thanks in advance.