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?

A solution mod $\,6\,$ remains a solution mod $\,3,\,$ yielding $\ 0\equiv 3x\equiv 1\pmod 3,\,$ contradiction.
