How to prove that 2 is not a Gaussian prime? – math.stackexchange.com

How to prove that 2 is not a Gaussian prime? – math.stackexchange.com

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To prove an algebraic number is not a Gaussian prime, need find factors of it. Let us assume, $(a + bi)(x +yi) = 2, \exists a,b,x,y \in \mathbb{Z}$; so $(ax -by) + i(ay + bx) =2$. As imaginary part ...

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