Congruence Modulo Integer/Examples/-2 equiv 14 mod 8

Example of Congruence Modulo an Integer

$-2 \equiv 14 \pmod 8$

Proof

By definition of congruence:

$x \equiv y \pmod n$ if and only if $x - y = k n$

for some $k \in \Z$.

We have:

$\paren {-2} - 14 = -15 = \paren {-2} \times 8$

Thus:

$-2 \equiv 14 \pmod 8$

$\blacksquare$

Sources

• 1964: Walter Ledermann: Introduction to the Theory of Finite Groups (5th ed.) ... (previous) ... (next): Chapter $\text {I}$: The Group Concept: $\S 6$: Examples of Finite Groups: $\text{(iii)}$