The SlugMath Wiki is under heavy development!
State/Multiplicative inverses exist mod p
In other words, the totient of $p$ is $p-1$: $\phi(p) = p-1$; there are $p$ residues, mod $p$, of which all but zero are invertible.
In other words, $\FF_p$ is a field.
This statement logically relies on the following definitions and statements: Def/Residue, Def/Invertible residue, State/Nonmultiples of a prime are relatively prime to the prime, State/Relative primality to the modulus is equivalent to invertibility of a residue
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