# Divisibility

• March 1st 2010, 11:13 AM
novice
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 $q$?
• March 1st 2010, 12:55 PM
hatsoff
Quote:

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.