Documentation

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.

Compare with the solution for Problems.P44:

$ stack bench --benchmark-arguments="P44/isGaussianPrime P45/isGaussianPrime'"

Examples

>>> isGaussianPrime' (0 :+ 5)
False

>>> isGaussianPrime' (17 :+ 0)
False

>>> isGaussianPrime' (5 :+ 2)
True