Existence of Primitive Element for every Prime

Theorem

Let $p$ be a prime number.

Then there exists a primitive element of the multiplicative group of reduced residues $\Z'_p$.

Proof

This theorem requires a proof. In particular: It needs to be demonstrated that $\Z'_p$ is cyclic, which Nelson assures us is "not elementary, and determining the smallest primitive element can be difficult." You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): primitive element