Definition 2.1. When a and b are integers, we say a divides b if b = ak for some k ∈ Z. We then write a | b (read as “a divides b”). Example 2.2. We have 2 | 6 (because 6 = 2 · 3), 4 | (−12), and 5 | 0. We have ±1 | b for every b ∈ Z. However, 6 does not divide 2 and 0 does not divide 5. Divisibility is a relation, much like inequalities. In particular, the relation 2 | 6 is not the number 3, e...
