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The number of generators of cyclic group of order 219 is __________(a) 144(b) 124(c) 56(d) 218I have been asked this question during an online interview.Enquiry is from Cyclic Groups topic in chapter Groups of Discrete Mathematics

Answer»

The CORRECT option is (a) 144

For explanation I WOULD say: The NUMBER of generators of a cyclic group of order N is equal to the number of integers between 1 and n that are relatively prime to n.Namely, the number of generators is equal to ϕ(n), where ϕ is the Euler totient function. We know that G is a cyclic group of order 219. Hence, the number of generators of G is ϕ(219) = ϕ(3)ϕ(73) = 3⋅73 = 144.



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