Pythagorean triples over Gaussian integers (Q2911230)

The authors define a set PT of Pythagorean triples in the ring of Gaussian integers as \((a,b,c) \in \mathbb{Z}[i]^3\), where \(a \neq 0\) and \(a^2+b^2=c^2\). The set PT is a commutative monoid under the operation \(*\) defined by NEWLINE\[NEWLINE(a_1,b_1,c_1) * (a_2,b_2,c_2)=(a_1a_2,b_1c_2+b_2c_1,b_1b_2+c_1c_2)NEWLINE\]NEWLINE with the identity element \((1,0,1)\). In the paper the authors derive some unique factorization theorem in PT and study some related questions.