Common Factor Cancelling in Congruence/Examples/6 equiv 12 mod 2 leads to 2 equiv 4 mod 2
Jump to navigation
Jump to search
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 $\text {4-5}$