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# State/There are no zero divisors mod p

Proposition: (There are no zero divisors mod p) Suppose that $p$ is a prime number. Suppose that $\bar x$ and $\bar y$ are residues mod $p$.

Then, if $\bar x \bar y = \bar 0$, then $\bar x = \bar 0$ or $\bar y = \bar 0$.

## Logical Connections

This statement logically relies on the following definitions and statements: Def/Prime number, Def/Residue, State/Multiplicative inverses exist mod p

The following statements and definitions rely on the material of this page: State/Half of nonzero residues are quadratic residues

To visualize the logical connections between this statements and other items of mathematical knowledge, you can visit the following cluster(s), and click the "Visualize" tab: Clust/Modular arithmetic