Chinese Remainder Theorem/Examples/n = 7 mod 12 so n = 3 mod 4

Example of use of Chinese Remainder Theorem
Let $n \equiv 7 \pmod {12}$.

Then:
 * $x \equiv 3 \pmod 4$

Proof
By the Chinese Remainder Theorem:


 * $n \equiv 7 \pmod {12} \iff n \equiv 7 \pmod 3 \text { and } n \equiv 7 \pmod 4$

as $3$ and $4$ are coprime.

Thus given the hypothesis: