Compute [phi](n) = (p-1)(q-1), where [phi] is Euler's

totient function.

They then proceeded, also immediately, without a pause, to factor 111 (a perfect

totient number) into the product of the prime number 37 multiplied by 3, prime numbers being the twins' life obsession.

If t is a

totient of N, then by definition no prime factor of t divides N.

mathematical expression not reproducible] P [member of] G are given, specify that d is a prime number and that [phi] is the Euler

totient function and that k is a generator of multiplicative cyclic group with order [phi](d); we can solve [alpha] [member of] [Z.

k] where [phi](n) is the Euler's

totient function and k is the number of distinct prime divisors of n.

where [phi](n) = #{m [member of] N: 1 [less than or equal to] m [less than or equal to] n, (m, n) = 1} is Euler's

totient function and [[omega].

In this section, we study the performance of our proposed algorithms and compare them with the Euler's

totient based Algorithm, MDS algorithm, secure group communication, one way function tree, Binary tree based, Efficient large group key distribution, and Logical key hierarchy Algorithm described in [1][5][9][10][12][23][24] which are labeled as ETF, MDS, SKDC, OFT, Binary, ELK and LKH respectively.

4] Chengliang Tian and Xiaoyan Li, On the Smarandache power function and Euler

totient function, Scientia Magna, 4(2008), No.

For a positive integer n, the Euler phi function (or Euler

totient function) [phi](n) is defined to be the number of positive integers less then n which are relatively prime to n.

We shall need the following property, an easy consequence of the previous considerations, of the Jordan

totient function:

e] mod N, where N is the product of two large prime numbers of same length, e is the public key chosen such that it is relatively prime with the Euler

totient function [phi](N) and 1 < e < [phi](N).

Euler's

Totient Function," "Does --(n) Properly Divide n-1," "Solutions of --(m)=--(n)," "Carmichael's Conjecture," "Gaps Between Totatives," "Iterations of --and--," "Behavior of --(--(n)) and --(--(n)).