Co to jest arytmetyka modularna?

$\dfrac{A}{B} = Q \text{ reszty } R$start fraction, A, divided by, B, end fraction, equals, Q, start text, space, r, e, s, z, t, y, space, end text, R

$\begin{array}{rcl}{\displaystyle \frac{13}{5}}& =& 2\text{ reszty }\mathbf{3}\\ 13\text{ mod }5& =& \mathbf{3}\end{array}$‍

$\begin{array}{rcl}\frac{0}{3}& =& 0\text{ reszta }\mathbf{0}\\ \frac{1}{3}& =& 0\text{ reszta }\mathbf{1}\\ \frac{2}{3}& =& 0\text{ reszta }\mathbf{2}\\ \frac{3}{3}& =& 1\text{ reszta }\mathbf{0}\\ \frac{4}{3}& =& 1\text{ reszta }\mathbf{1}\\ \frac{5}{3}& =& 1\text{ reszta }\mathbf{2}\\ \frac{6}{3}& =& 2\text{ reszta }\mathbf{0}\end{array}$‍

$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

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

-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