[Theorem 5.1] If a prime number p divides ab, then p divides either a or b. [Proof] (a, p) is a divisor of p, so it's either 1 or p. Two cases: 1. (a, p) = p, therefore p divides a, Q.E.D. 2. (a, p) = 1. Then with theorem 2.3, we can show that p divides b. Q.E.D.
[Definition 5.1] For any natural number greater than 2, the "non-trivial divisor" is defined as any divisor other than 1 and itself. If a natural number greater than 2 has 1 or more non-trivial divisors, it is a composite number. Otherwise, it is a prime number.
*Since we are discussing the concept of divisibility, it is not necessary to take into account negative numbers. However, to make the concept of minimality well-defined, the rest of this book will discuss natural numbers only.
Of course not!
Is 9 a prime?
You can't be deceived!
The Ice Fairy at the lake said Prime numbers are "awesome numbers" and glossed it over!
<a href="http://en.wikipedia.org/wiki/Prime_number">Prime number</a>
Prime number
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