Introduction to Number Theory
Number theory is the study of the properties of numbers. It is one of the oldest branches of mathematics, and dates back to ancient Greece. Number theory is a very abstract branch of mathematics, and is not always easy to understand. However, it can be very rewarding to study, as it can lead to some very deep and interesting results.
One of the most basic properties of numbers is the division theorem. This theorem states that, for any two numbers a and b, there exists a unique number c such that a = c*b. This theorem is the basis for many other results in number theory.
Another basic property of numbers is the commutative law of addition. This law states that the order of addition does not affect the result. That is, for any two numbers a and b, a + b = b + a.
There are a number of other basic properties of numbers, which are listed below.
– Associative law of addition: a + (b + c) = (a + b) + c
– Commutative law of addition: a + b = b + a
– Identity law of addition: a + 0 = a
– Inverse law of addition: For every number a there exists a number b such that a + b = 0
There are also a number of basic properties of multiplication, which are listed below.
– Associative law of multiplication: a*(b*
