Find all prime numbers $y$ and $z$ if $x$ is an integer and $x^2-y^2-z^2=2017.$ Find prime numbers $y$ and $z$ if $x$ is an integer and $x^2-y^2-z^2=2017.$

$x^2-y^2-z^2$ is not factorable, so what should I do?  My mind is blank here.  Any help is appreciated.

We have that $$a^2\equiv 1\lor  0\pmod{4}$$
We also have that $$2017\equiv 1\pmod{4}$$.Now try to choose $x^2,y^2,z^2$ so that you get $1\pmod{4}$.You can see that the only solution is if $y^2\equiv 0\pmod{4}$ and $z^2\equiv 0\pmod{4}$ but since $z,y$ are prime we have that $z=y=2$ so the only solution is
$x^2-8=2017,x^2=2025,x=45$
