Common Factor Cancelling in Congruence/Examples/6 equiv 12 mod 2 leads to 2 equiv 4 mod 2

Example of Common Factor Cancelling in Congruence

We have that:

$6 \equiv 12 \pmod 2$

and so:

$2 \equiv 4 \pmod 2$

Proof

\(\ds 6\)

\(\equiv\)

\(\ds 12\)

\(\ds \pmod 2\)

\(\ds \leadsto \ \ \)

\(\ds 2 \times 3\)

\(\equiv\)

\(\ds 4 \times 3\)

\(\ds \pmod 2\)

\(\ds \leadsto \ \ \)

\(\ds 2\)

\(\equiv\)

\(\ds 4\)

\(\ds \pmod 2\)

as $\gcd \set {2, 3} = 1$

Sources

• 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {4-1}$ Basic Properties of Congruences: Example $\text {4-5}$