Also, we know that \( x^{2}=y+z^{2} \).
We can rearrange the equation to find \( y \), which gives us \( y = x^{2} - z^{2} \).
This can be factored into \( y = (x-z)(x+z) \).
Since \( y \) is a prime number, it only has two factors: 1 and itself. This means
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