Multiplication mod n

The multiplication table of $\mathbb{Z}/n$, one cell per product: row $i$, column $j$, holding $ij \bmod n$. Colored by what the product is, its structure shows at a glance: the units make a Latin square, the idempotents mark how $n$ splits by the Chinese remainder theorem, and the square roots of each residue sit on the diagonal. A $1$ in the cell $(x, x - k)$ says $x(x - k) = 1$: $x$ is a root of $x^2 - kx - 1$, a metallic mean of $\mathbb{Z}/n$.

Multiplication in , n = , its elements listed : units by their multiplicative order, the one white, idempotents gold, nilpotents red, other zero divisors faint. Selecting a cell lights its ; shift-click to select several.