Product of units modulo m Help!!! I can find units in a given $Z_m$ manually by testing out every single value which is relative to m,,, but in general I do not know a way how to find such units... hence I cant answer this question: Prove that the product of units mod m is congruent to $\pm 1$ mod m.
Any idea?

If the class of of $[p]$ is invertible mod $m$, $a'p=am+1$ or $am-1$, you have
$(am+1)(bm+1)=m(mab+a+b)+1, (am+1)(bm-1)=m(abm-a+b)-1$
$ (am-1)(bm-1)=m(abm-a-b)+1$. This shows the product of two invertible numbers mod $m$ is $1$ mod $m$ or $-1$ mod $m$.
