1. ## Modulo arithmetic

Hey, just stuck on this question:

Show that in $\displaystyle Z_m$ we have $\displaystyle (m-1)^{-1} = m-1$

I have no idea. Please help! $\displaystyle Z$ is used to represent the set of integers.

2. Originally Posted by Joel24
Hey, just stuck on this question:

Show that in $\displaystyle Z_m$ we have $\displaystyle (m-1)^{-1} = m-1$

I have no idea. Please help! $\displaystyle Z$ is used to represent the set of integers.
Well there exists only one multiplicative inverse to any element of $\displaystyle \mathbb{Z}_m$. So let's find out if the identity works:
$\displaystyle (m - 1)^{-1}(m - 1) = (m - 1)(m - 1) = m^2 - 2m + 1 \equiv 1~\text{mod m}$

It looks like the original assumption is true.

-Dan

3. Yes, that makes sense. Thanks a lot Dan.