Originally Posted by

**demode** Prove that the mapping $\displaystyle \pi (i) = 328 i \mod 2011$ is a permutation of $\displaystyle S_{2011}$.

__Attempt:__

I think to prove this I have to show that both one-to-one and onto properties hold:

For one-to-one, suppose $\displaystyle \pi(i_1)=\pi(i_2)$

$\displaystyle 328 i_1 \mod 2011 = 328 i_2 \mod 2011$

Now how do I simplify this to get $\displaystyle i_1 =i_2$?

To prove it's Onto, I think I have to show that evey $\displaystyle i$ has an image under $\displaystyle \pi$. So, how do I need to "show" that $\displaystyle \pi(i) = 328 i \mod 2011=j$ for some j?