Congruence Modulo Integer/Examples/2 equiv -6 mod 4
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Example of Congruence Modulo an Integer
- $2 \equiv -6 \pmod 4$
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:
- $2 - \paren {-6} = 8 = 2 \times 4$
Thus:
- $2 \equiv -6 \pmod 4$
$\blacksquare$
Sources
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $1$: Integral Domains: $\S 6$. The Residue Classes: Example $8$