Math Help - Divisibility

1. Divisibility

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

2. Originally Posted by novice
Since it is commonly known that if an integer $x$ is not divisible by 3, then $x = 3q + 1$ or $x = 3q + 2$, does it mean that if an integer $y$ is not divisible by 11, then $y = 11q + 1$ or $y = 11q+2$ or $y=11q + 3$or …or $y = 11q+10$ for some integer $q$?
Yes. You may read about the division algorithm to understand why this must be the case.