Definition:Composite Gaussian Integer

Definition

Let $x \in \Z \sqbrk i$ be a Gaussian integer.

$x$ is defined as being composite if and only if it is the product of two Gaussian integers, neither of which is a unit (that is, $\pm 1$ or $\pm i$).

Examples

The following are examples of composite Gaussian integers:

\(\ds 2\)

\(=\)

\(\ds \paren {1 + i} \paren {1 - i}\)

\(\ds 46 + 9 i\)

\(=\)

\(\ds \paren {5 + 12 i} \paren {2 - 3 i}\)

\(\ds 5 + 12 i\)

\(=\)

\(\ds \paren {3 + 2 i}^2\)

Also see

• Definition:Gaussian Prime

• Results about composite Gaussian integers can be found here.

Source of Name

This entry was named for Carl Friedrich Gauss.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Gaussian integer
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Gaussian integer