Definition:Composite Gaussian Integer
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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
- 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