Discrete Mathematics Number theory

The focus of this entire note is on positive integers. I will start by the basic notion of divisibility. We say that a divides b, or a is a divisor of b, or b is a multiple of a, if there exists an integer m such that b = am We also denote this by a | b (a divides b). If a is not a divisor of b, the we write a | b, but we can still talk about division by a with a remainder r. Given any two integers a and b, there is a unique way to write (q and r are integers)