Take the 2-minute tour ×  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?
share|improve this question Presumably, you mean all but one of
them has order 2. –  Gerry Myerson Nov 28 '12 at 12:16 yupp bar
the number 1, could you confirm ive answered it correctly or
have i gone terribly wrong? –  jill Nov 28 '12 at 12:18 @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 $2$ – 
Cocopuffs Nov 28 '12 at 12:27  2 Answers 2
$(2a+1)^2=4a^2+4a+1=8\frac{a(a+1)}2+1\equiv \pmod 8\implies
c^2\equiv1\pmod 8$ if $(c,8)=1$  Now, $(3b\pm1)^2\equiv 1\pmod
3\implies