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Using Fermat's two-square theorem, it can be shown that a Gaussian integer \(a+bi\) is prime if and only if it falls into one of the following categories:

• |a| is prime and \(|a| \equiv 3 \mod 4\), if \(b=0\).
• |b| is prime and \(|b| \equiv 3 \mod 4\), if \(a=0\).
• \( a^2 + b^2 \) is prime, if \( a \neq 0 \) and \( b \neq 0 \).

Use this property to determine whether a Gaussian integer is a Gaussian prime.