I was reading a paper and I am struggling understanding one part of it. Lets say we have a group $G$ of an unknown order $n$. we know that $B<n<B+C$. both B and C are large values).
we choose a random element $z \in G$. and let's say we have some prime values $B+C<e_1,e_2,...,e_l$. We Calculate $h=z^ {\prod_i e_i}$.
The claim is as $\gcd(n,\prod e_i)=1$ (which is true as each prime is greater than $n$) we can say that $h$ is uniformly distributed in $G$. How can we prove this statement?