Solution of Linear Congruence/Examples/6 x = 5 mod 4

Example of Solution of Linear Congruence
Let $6 x = 5 \pmod 4$.

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

Proof
Using the Euclidean Algorithm:

Thus we have that:
 * $\gcd \set {6, -4} = 2$

which is not a divisor of $5$.

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