Common Factor Cancelling in Congruence/Examples/6 equiv 12 mod 2 does not lead to 3 equiv 6 mod 2

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Example of Common Factor Cancelling in Congruence

We have that:

$6 \equiv 12 \pmod 2$

but:

$3 \not \equiv 6 \pmod 2$


Proof

\(\ds 6\) \(\equiv\) \(\ds 12\) \(\ds \pmod 2\)
\(\ds \leadsto \ \ \) \(\ds 2 \times 3\) \(\equiv\) \(\ds 2 \times 6\) \(\ds \pmod 2\)
\(\ds \not \leadsto \ \ \) \(\ds 3\) \(\equiv\) \(\ds 6\) \(\ds \pmod 2\) as $\gcd \set {2, 6} \ne 1$

$\blacksquare$


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