A way of finding $x \in \mathbb{Z}$, congruency I'm trying to find all $x \in \mathbb{Z}$ that satisfies this equation
$$3x  \equiv 1 \pmod 6$$

I tried using trial and error, but couldn't find a suitable number for x.
I know that the $\mbox{gcd}$ is $3$.
How would I approach this?

There is no such $x,k\in Z$ such that $3(x-2k)=1$ is satisfied.
