Congruence Modulo Integer/Examples/-3 equiv -5 mod 2

Example of Congruence Modulo an Integer

$-3 \equiv -5 \pmod 2$

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:

$-3 - \paren {-5} = 2 = 1 \times 2$

Thus:

$-3 \equiv -5 \pmod 2$

$\blacksquare$

Sources

• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 2.5$. Congruence of integers: Example $38$