Cyclic group

Question

If (G,*) is a cyclic group of order 81 then number of generators in G is????

Answer 1

54 Generators

 

Formula used :   if Φ(Pⁿ) = Pⁿ - P^n-1 , P is Prime Number

 

Another case: 

If n is some number and if we can split n in such a way that it becomes multiplication of two prime numbers.

n = p * q

Φ(n) = Φ(p) * Φ(q) = (p-1) * (q-1) , here p and q are Prime Numbers

 

Φ(n) is Euler's Totient Function

https://en.wikipedia.org/wiki/Euler%27s_totient_function

Comments

Karan Dodwani 1

The Prime Factorization is:
2 x 2 x 3 x 7

Totient Function (2^2) = (2^2 - 2^1)=2
Totient Function (3)=2
Totient Function (7)=6

Totient Function (84) = 2*2*6 = 24

 

you can check here: http://www.javascripter.net/math/calculators/eulertotientfunction.htm

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Thanks @Aakash_