Given an integer
![{n>1}](/media/m/2/0/c/20cd7d1dc55ea9b07802f153a5a547e8.png)
, denote by
![P_{n}](/media/m/3/e/3/3e3e3d11fc42db7865977168b42953d3.png)
the product of all positive integers
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
less than
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
and such that
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
divides
![{x^2-1}](/media/m/3/0/f/30fab8f2bf81aea9eeae12d7eb7cd80d.png)
. For each
![{n>1}](/media/m/2/0/c/20cd7d1dc55ea9b07802f153a5a547e8.png)
, find the remainder of
![P_{n}](/media/m/3/e/3/3e3e3d11fc42db7865977168b42953d3.png)
on division by
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
.
%V0
Given an integer ${n>1}$, denote by $P_{n}$ the product of all positive integers $x$ less than $n$ and such that $n$ divides ${x^2-1}$. For each ${n>1}$, find the remainder of $P_{n}$ on division by $n$.