# Unique Factorization Theorem for Gaussian Integers

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## Theorem

For every Gaussian integer $n$ such that $\left\vert{n}\right\vert > 1$, $n$ can be expressed as the product of one or more Gaussian primes, uniquely up to the order in which they appear.

## Historical Note

This result, and the ideas associated with it, ushered in the field of algebraic number theory.