Congruence Modulo Integer/Examples/-10 equiv 8 mod 6
Jump to navigation
Jump to search
Example of Congruence Modulo an Integer
- $-10 \equiv 8 \pmod 6$
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:
- $-10 - 8 = -18 = \paren {-3} \times 6$
Thus:
- $-10 \equiv 8 \pmod 6$
$\blacksquare$
Sources
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 2.5$. Congruence of integers: Example $38$