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CSS Pure Mathematics QUESTION #4102
Question 1
The order of element \(4\) in the cyclic group \(\mathbb{Z}_{18}\) is:
  • \(9\)✔️
  • \(4\)
  • \(6\)
  • \(18\)
Correct Answer Explanation
The order of element \(k\) in \(\mathbb{Z}_n\) is \(\dfrac{n}{\gcd(k,n)}\). Here: \(\dfrac{18}{\gcd(4,18)}=\dfrac{18}{2}=9\). So element \(4\) has order \(9\) in \(\mathbb{Z}_{18}\).