Review of Number Theory

Z = set of integers {$\cdots$, -2, -1, 0, 1, 2, $\cdots$}
N = set of natural numbers {0, 1, 2, $\cdots$}

For two integers d and a, d $\mid$ a (d divides a) if a = kd, k $\in$ Z. In this case, a is a multiple of d, and d is a divisor of a (if d >= 0). Every integer divides 0.

Examples: 2 $\mid$ 8, 3 $\mid$ 9, 2 $\mid$ 10

Every integer a has the trivial divisors 1 and a.

Nontrivial divisors are called factors.

Examples: 2 is a factor of 8 and 10, 3 is a factor of 9.

An integer a > 1 with only trivial divisors is a prime number; otherwise, a is a composite. The integers {$\cdots$, -2, -1, 0, 1} are neither prime nor composite. There are infinitely many prime numbers.