# Math Help - Primitive root problem

1. ## Primitive root problem

Suppose that n has a primitive root. Show that $\prod _{1 \leq d \leq n } d \equiv -1 \ (mod \ n)$, where gcd(d,n) = 1.

Suppose that n has a primitive root. Show that $\prod _{1 \leq d \leq n } d \equiv -1 \ (mod \ n)$, where gcd(d,n) = 1.
Let $r$ be the primitive root for $n$ then it means $\prod_{d=1}^n d \equiv \prod_{k=1}^n r^k = r\cdot r^2 \cdot ... \cdot r^n = r^{n(n+1)/2}(\bmod n)$.