Main Index Number Theory Sequences Primes
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Standard form

The Fundamental Theorem of Arithmetic says that any integer typeset structure greater than 1 can be written as a unique product (up to ordering of the factors) of prime numbers, say

n = q _ 1 q _ 2 ...q _ s .(1)

The primes in (1) are not necessarily distinct, nor are arranged in a particular form. If we arrange them in increasing order and associate single equal primes into powers, and change the notation appropriately, we obtain   

n = p _ 1^α _ 1 p _ 2^α _ 2 ...p _ k^α _ k    ,   & ... ; ... < p _ k ,    α _ 1 > 0, α _ 2 > 0, ... , α _ k > 0 .(2)

We then say that typeset structure is written (or expressed) in standard form.

To factorize a positive integer go to .

Cite this web-page as:

Štefan Porubský: Standard Form.

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