TITLE: Gaussian Integer a+2bi as sum of 3 squares
QUESTION [9 upvotes]: Let $a, b \in \mathbb{Z}$. Then is it true that the Gaussian integer $a+2bi$ can be expressed as a sum of three squares?

REPLY [4 votes]: The question is not new. See my old question and its answer available from Is it true that $\{x^4+y^2+z^2:\ x,y,z\in\mathbb Z[i]\}=\{a+2bi:\ a,b\in\mathbb Z\}$?