I've been reading about p-adics and I think I understand most of the basics (Thanks to David A. Madore's "A First Introduction to p-adic Numbers" found at http://www.madore.org/~david/math/padics.pdf).
I need some clarification (maybe an example would help) on how to get the inverse of a p-adic integer.
The method used (in the paper) is for getting the inverse of . So, if you have a p-adic integer, say , which ends in , you have to let , and solve for , which will end with a . Then the inverse of . Is this the correct way of getting the inverse of ?
Now, if ends in something else other than zero or one, what we are supposed to do is look for a digit so that will end in a one, and thus can be inverted by the above method (if it's correct ). Since we have the inverse of , to get the inverse of , we multiply the inverse of by again. Is this correct?