Formula for the Number of Units in a Ring Modulo a Prime Power

[mathmajor2013]

So the question is:

Suppose p is a prime and n is a positive integer. Find a formula for |(Z/p^nZ)^x|.

I do not know what this notation means, what do the | | mean around this? I know that the other part is the set of all the units in Z/p^nZ, but I have no idea what the | | mean. I don't think it's absolute value. Is it just the elements of it? Thanks for the help.

 

[CRGreathouse]

I do not know what this notation means, what do the | | mean around this?

"The number of elements in". |{2, 4, 6}| = 3.

 

[Outlined]

Do you mean this:

$$|({\textbf{Z}} / p^{n}{\textbf{Z}})^{*}|$$

in words: the number of units in the ring $${\textbf{Z}} / p^{n}{\textbf{Z}}$$

(suggestions: if would like to avoid the tex tag you can use the sup tag to write down your statements: |(Z/pⁿZ)^x|
)