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I have the question:
compute $\phi(24)$ for each element Z/24 decide whether the element is a unit or a zero divisor, if the element is a unit divisor give its order and find its inverse.

Ive worked out $\phi(24)=8$
and the unit divisors to be ${1,5,7,11,13,17,19,23}$
however when I came to working out the order I got them all to be 2?

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    Presumably, you mean all but one of them has order 2.2012-11-28
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    yupp bar the number 1, could you confirm ive answered it correctly or have i gone terribly wrong?2012-11-28
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    @jill You can write $(\mathbb{Z}/24)^{\times} \cong (\mathbb{Z}/8)^{\times} \times (\mathbb{Z}/3)^{\times} \cong \mathbb{Z}/2 \times \mathbb{Z}/2 \times \mathbb{Z}/2$ in which it's easy to see that all elements have order at most $2$2012-11-28

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