When it comes to basic number theory, then we divisible from the set theory began to talk.
▎ divisible
☞ "define"
If a can b divisible, that is no remainder, we say a divides b, b is known as a divisible, denoted by a | b.
Where "|" called divisible symbol.
☞ "nature"
① reflexivity: Obviously, for any positive integer n, there are n | n;
② transitive: if a | b, b | c, there is a | c;
③ antisymmetry: if a | b, b | a, there is a = b;
Wherein ③ useful properties, generally for not prove a direct case of a = b, but little used.
And multiple divisors ▎
☞ "define"
If a | b, then a number is about b, b is a multiple of b is also known as a factor / factor.
☞ "inference"
Any number n has two trivial factors (except 1), i.e. 1 and n;
The remaining non-trivial factor called factor.
▎ prime and composite numbers
☞ "define"
Set a positive integer p ≠ 0,1. If it's in addition to 1 and no other divisors p, then p is called a prime number, otherwise composite number.
☞ "inference"
If a is a composite number, then a can be represented as a = pq, where p, q> 1, then p and q must have no more than a √A, so there is determined whether the number is a prime number O (√N )algorithm.