0 votes 0 votes If (G,*) is a cyclic group of order 81 then number of generators in G is???? saumya mishra asked Jul 16, 2018 saumya mishra 2.0k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 votes 54 Generators Formula used : if Φ(Pn) = Pn - Pn-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 Aakash_ answered Jul 16, 2018 • edited Jul 16, 2018 by Aakash_ Aakash_ comment Share Follow See all 2 Comments See all 2 2 Comments reply Aakash_ commented Aug 8, 2018 reply Follow Share 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 1 votes 1 votes Karan Dodwani 1 commented Aug 13, 2018 reply Follow Share Thanks @Aakash_ 0 votes 0 votes Please log in or register to add a comment.