Integers and Division

If a and b are integers with a0, then "a divides b" if there is an integer c such that b = ac. In this case a is a factor of b and b is a multiple of a.

We use the notation a | b to say "a divides b".

Theorem: Let a, b and c be integers. Then

1. if a | b and a | c then a | (b+c).
2. if a | b then a | bc for all integers c.
3. if a | b and b | c then a | c.