Was ist modulare Arithmetik?

$\dfrac{A}{B} = Q \text{ remainder } R$start fraction, A, divided by, B, end fraction, equals, Q, start text, space, r, e, m, a, i, n, d, e, r, space, end text, R

$\begin{eqnarray} \dfrac{13}{5} &=& 2 \text{ Rest } \bf{3} \\ 13 \text{ mod } 5 &=& \bf{3} \\ \end{eqnarray}$

$\begin{eqnarray} \frac{0}{3} &=& 0 \text { Rest } \bf{0} \\\frac{1}{3} &=& 0 \text { Rest } \bf{1} \\ \frac{2}{3} &=& 0 \text { Rest } \bf{2} \\ \frac{3}{3} &=& 1 \text { Rest } \bf{0} \\ \frac{4}{3} &=& 1 \text { Rest } \bf{1} \\ \frac{5}{3} &=& 1 \text { Rest } \bf{2} \\ \frac{6}{3} &=& 2 \text { Rest } \bf{0} \end{eqnarray}$

$8 \text{ mod } 4 = ?$8, start text, space, m, o, d, space, end text, 4, equals, question mark

$7 \text{ mod } 2 = ?$7, start text, space, m, o, d, space, end text, 2, equals, question mark

$-5 \text{ mod } 3 = ?$minus, 5, start text, space, m, o, d, space, end text, 3, equals, question mark

$\begin{eqnarray} 3 \text{ mod } 10 = 3 \\ 13 \text{ mod } 10 = 3 \\ 23 \text{ mod } 10 = 3 \\ 33 \text{ mod } 10 = 3 \\ \end{eqnarray}$

-5 % 3 = -2.

$A \equiv B\ (\text{mod } C)$A, \equiv, B, space, left parenthesis, start text, m, o, d, space, end text, C, right parenthesis