0 votes 0 votes What is the number of generators in a group G, such that Ο(G) = 87? pream sagar asked Jan 26, 2019 pream sagar 1.1k views answer comment Share Follow See all 15 Comments See all 15 15 Comments reply Magma commented Jan 26, 2019 reply Follow Share 84 0 votes 0 votes pream sagar commented Jan 26, 2019 reply Follow Share ans given by me is 86 0 votes 0 votes Magma commented Jan 26, 2019 reply Follow Share answer given is wrong 0 votes 0 votes pream sagar commented Jan 26, 2019 reply Follow Share please explain 0 votes 0 votes Magma commented Jan 26, 2019 reply Follow Share the number is co- prime to 87 are generator 3 and 29 are the not a co-prime number 1 , 2, 4 ....... 86 ----- > there are total 84 elements and if a number is prime no : ex = 23 then number of generator = (23-1) = 22 1 votes 1 votes Shubhgupta commented Jan 26, 2019 reply Follow Share you mean to say (9,87) are co-prime. co- prime are those numbers which are having GCD as 1. No of generators= eular function of n $\phi(n)$. 87= 3*29= (3-1)*(29-1)=2*28=56 5 votes 5 votes pream sagar commented Jan 26, 2019 reply Follow Share i had seen some expression to find out the no of generator ? if a, b are two prime factor other than 1 of oder (n) then no of generator is n*(1-1/a)(1-1/b) is it true 0 votes 0 votes Magma commented Jan 26, 2019 reply Follow Share I didn't understand @Shubhgupta acc to you what is answer ?? 0 votes 0 votes Shubhgupta commented Jan 26, 2019 reply Follow Share @pream sagar, yes both are same thing. after simplification you'll get same thing. @Magma, you are saying 3 and 29 are not co-prime to 87 and all are co-prime. but according to definition of co prime, co- prime are those numbers which are having GCD as 1. like in (9,27) GCD is 3 not 1. and 56 is right answer. 0 votes 0 votes Magma commented Jan 26, 2019 reply Follow Share you are saying 3 and 29 are not co-prime to 87 and all are co-prime. but according to definition of co prime, co- prime are those numbers which are having GCD as 1. like in (9,27) GCD is 3 not 1. I'm saying the number which is co-prime to 87 means (1,87) , (2,87) , (4,87) .... (86,87) (3,87) ---> not a co-prime no similarly for 29 answer is 84 0 votes 0 votes Shubhgupta commented Jan 26, 2019 reply Follow Share according to you (9,87) is co prime or not? 0 votes 0 votes gauravkc commented Jan 26, 2019 reply Follow Share @Shubhgupta A small help here. Can u give some reference for the euler function. How it's calculated. 0 votes 0 votes Magma commented Jan 26, 2019 reply Follow Share Not it's not :p 0 votes 0 votes Shubhgupta commented Jan 26, 2019 reply Follow Share @gauravkc, check this- https://gateoverflow.in/3780/gate2005-it-34?show=101261#a101261, wiki link explains this very well. 1 votes 1 votes balchandar reddy san commented Jan 30, 2019 reply Follow Share Number of numbers which are less than 87 and not co-prime to 87 are: 1) all multiples of 3 under 87= 28 2) all multiples of 29 under 87 = 2 Since, 3 and 29 are the only 2 prime factors of 87 So the number of generators are: 86 - 30 = 56. 0 votes 0 votes Please log in or register to add a comment.