A primal approach

Number Theory Level pending

Assuming that the following equation has answers over \( x,y,z \in \mathbb {z} \) for \(p\) as a prime number,how many different values can \(y-z\) have?

\(y({z^2}-{x^2}) + x({y^2}-{z^2}) + z({x^2}-{y^2}) =p \)

By the way my own choice of difficulty was "Level 4" but well since it's locked, the question remains "Level 3" for the time being.

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