PhiSigma Essay

This essay has a total of 276 words and 6 pages.

PhiSigma



Phi and Sigma

This purpose of this paper is to investigate Eulerís Phi ( ) function. Eulerís phi
function, (n), is the number of numbers greater than (n) and relatively to (n).

For Example:
(12)=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12}=[4]
(12)=[4]
The phi of [12] is [4] because there are four divisors between 1-12 whose GCD (greatest
common divisor) with [12] is one. To be able to find (n) for larger numbers we must first
define the prime factorization of (n) and apply it to the formula where (n) represents the
number and (P) represents the prime.


Therefore:
(N)=

f(12)=[4]

4 * 3

2 * 2
=2 *3
Another function used in number theory is the sigma function. For example, (6)=(12)
because the factors of 6 are (1, 2, 3, 6). If we add these numbers together we get (1 2 3
6=12). Sigma for large number can be calculated by utilizing the formula below.


(N)= * Ö

Example:
(144)

12*12

4*3 4*3

2*2 2*2
=2 *3

* = *
*
*

31*13=403
There are procedures where where (n) is not equal to (m) sentence. Below is a list of
values for which sigma; (n)=phi;(m).


The offline program maple V are used to generate:
Sigma;(n)=phi;(m)



4=4

6=6

12=12

8=8

18=18
Continues for 3 more pages >>