Kongruencje - krótkie pytanie

[musialmi]

Dlaczego \(\displaystyle{ x \equiv 5 \mod 6 \implies x \equiv 1 \mod 2 \wedge x \equiv 2 \mod 3}\)?

[Igor V]

\(\displaystyle{ x \equiv 5 \mod 6 \implies x-5=6k \ k\in\ZZ}\)
\(\displaystyle{ x-1=6k+4=2(3k+2) \Rightarrow x \equiv 1 \mod 2}\)
\(\displaystyle{ x-2=6k+3=3(2k+1) \Rightarrow x \equiv 2 \mod 3}\)