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CSS Pure Mathematics QUESTION #4114
Question 1
How many distinct group homomorphisms $\varphi: \mathbb{Z}_6 \to \mathbb{Z}_6$ exist?
  • $2$
  • $4$
  • $6$✔️
  • $12$
Correct Answer Explanation
Homomorphisms from $\mathbb{Z}_m$ to $\mathbb{Z}_n$ correspond to elements whose order divides $m$. Number is $\gcd(6,6) = 6$.