Congruence Modulo Integer/Examples/8 equiv 2 mod 2

Example of Congruence Modulo an Integer

$8 \equiv 2 \pmod 2$

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:

$8 - 2 = 6 = 3 \times 2$

Thus:

$8 \equiv 2 \pmod 2$

$\blacksquare$

Sources

• 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {4-1}$ Basic Properties of Congruences: Example $\text {4-1}$