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

(12)={1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 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. f(12)=[4] 2 * 2 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. 12*12

2*2 2*2 =2 *3 * 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:

### The Term Paper on African American Fraternity, Phi Beta Sigma

The most remarkable leadership in the African American community in the 20th century without question came from the ranks of Phi Beta Sigma Fraternity, Inc. (FBS). Since our founding on January 9, 1914, at Howard University in Washington, DC, we have supplied an empowering voice and vision to the struggle of African Americans and people of color around the world.The idea behind a fourth historical ...