Congruence Modulo Integer/Examples/100 equiv -40 mod 20
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Example of Congruence Modulo an Integer
- $100 \equiv -40 \pmod {20}$
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:
- $100 - \paren {-40} = 140 = 7 \times 20$
Thus:
- $100 \equiv -40 \pmod {20}$
$\blacksquare$
Sources
- 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {4-1}$ Basic Properties of Congruences: Example $\text {4-1}$