Congruence Modulo Integer/Examples/13 equiv 3 mod 5
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Example of Congruence Modulo an Integer
- $13 \equiv 3 \pmod 5$
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:
- $13 - 3 = 10 = 2 \times 5$
Thus:
- $13 \equiv 3 \pmod 5$
$\blacksquare$
Sources
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 2.5$. Congruence of integers: Example $38$