# Thread: Multiplicative inverse of n

1. ## Multiplicative inverse of n

Hi all, I have problem with the question: Find a multiplicative inverse of n in Z(n^2 -1) (or mod n^2 -1).
I think I can't use "Reverse the Euclidean algorithm" or matrices to find n^-1.
I would be thankful for your helping. Thanks a lot.

2. ## Re: Multiplicative inverse of n

Umm, $n^2 = (n^2-1)+1$ So, $n^{-1} \equiv n \pmod{n^2-1}$