(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] group theory problem

1. The problem statement, all variables and given/known data

A cyclic group of order 15 has an element x such that the set {x^3,x^5,x^9} has exactly two elements. The number of elements in the set {x^{13n} : n is a positive integer} is

a)3

b)5

2. Relevant equations

3. The attempt at a solution

From the given information, we know that x^6 = 1 or x^4 = 1. In the first case, either answer is possible. In the second case, only answer a is possible. Anyway, do we know enough to decide which case this is or is there a different way to do the problem?

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# Homework Help: Group theory problem

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