Congruence Modulo Integer/Examples/3 equiv 15 mod 4

Example of Congruence Modulo an Integer

$3 \equiv 15 \pmod 4$

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:

$3 - 15 = -12 = \paren {-3} \times 4$

Thus:

$3 \equiv 15 \pmod 4$

$\blacksquare$

Sources

• 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $1$: Integral Domains: $\S 6$. The Residue Classes: Example $8$