Since it is commonly known that if an integer $\displaystyle x$ is not divisible by 3, then $\displaystyle x = 3q + 1$ or $\displaystyle x = 3q + 2$, does it mean that if an integer $\displaystyle y$ is not divisible by 11, then $\displaystyle y = 11q + 1$ or $\displaystyle y = 11q+2$ or $\displaystyle y=11q + 3 $or …or $\displaystyle y = 11q+10 $ for some integer $\displaystyle q$?