Moreover, let q denote the least common multiple of the periods [q.sub.1], ..., [q.sub.r1], and let [[eta].sub.1], ..., [[eta].sub.r] be the reduced residue system modulo q, where r = [phi](q) is the Euler
totient function.
Rivest-Shamir-Adleman (RSA) encryption algorithm which is based on the combination of prime factorization, Euler's
totient function, Euler's
totient theorem and Extended Euclidean Algorithm (EEA) is used to compute the private key for decryption process.
Then [[phi].sub.k](n) := (f * [sub.k]g)(n) is the analogue of the Euler
totient function.
* Compute [phi](n) = (p-1)(q-1), where [phi] is Euler's
totient function.
The Euler
totient function [phi](n) is defined to be equal to the number of positive integers less than n which are relatively prime to n.
Now, let [empty set] be the Euler
totient function, which is an arithmetic function
We need the following estimate of Thangadurai and Vatwani [8] which relates the cyclotomic polynomial [[PHI].sub.n] (x) with the Euler
totient function [phi].
The box spilled its contents, and the twins instantly, in unison, exclaimed, "111!" 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.
Then s(n) [less than or equal to] (n[phi](n))/[2.sup.k] where [phi](n) is the Euler's
totient function and k is the number of distinct prime divisors of n.