Solution of Linear Congruence/Examples/12 x = 9 mod 6

Example of Solution of Linear Congruence
Let $12 x = 9 \pmod 6$.

Then $x$ has no solution in $\Z$.

Proof
We have that:

Then we have that:
 * $\gcd \set {12, -6} = 6$

which is not a divisor of $9$.

So, from Solution of Linear Diophantine Equation, no solution exists.