Basic theorem of arithmetic

Basic theorem of arithmetic

The fundamental theorem of arithmetic , also known as the only decomposition theorem of positive integers , is that each natural number greater than 1 can be written as a product of prime numbers, and these factors are arranged by size, only one way. For example:.

The contents of the arithmetic basic theorem consist of two parts:

• The existence of decomposition:
• The uniqueness of decomposition, even if does not consider the order of permutations, the way that positive integers are decomposed into prime numbers is unique.

The basic theorem of arithmetic is a basic theorem in elementary number theory, and it is also the logical support point and starting point of many other theorems.

Application (1) a positive integer greater than 1 N, if its standard decomposition is: Then its positive number is (2) its sum of all positive factors is then called n is a complete number. The existence of odd perfect numbers is a conjecture that has not been resolved so far.

Basic theorem of arithmetic