About the prime divisor of a quadratic function

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Encountered in Modell's book Diophantine Equations.

In the second chapter, page 3, it says:

'every prime divisor of $p$ of $x^2-a$ for integer $x$ is either a divisor of $a$, or can be represented by a finite number of arithmetic progressions.' Where $x$ and $a$ mentioned should be considered as positive integers.

I don't quite get this claim, I am not even sure about whether the $x$ mentioned is a variable or constant, either doesn't make sense to me though.

Could somebody kindly explain this to me?