Sorry if this question is confusing, I'm still confused by the whole thing.
I'm trying to understand how RSA encryption works, but I'm having trouble with the modulus part. For RSA to work, $c=m^e \bmod n$ must give an unique $c$ as long as $0<m<n$. I'm trying to find a pattern for the combinations of $e$ and $n$ that produce an unique $c$ for each $m$. I'm having trouble find any patterns.
When I tried $e=3$, $n=2,3,5,6,10,11,15,17$ all produce unique $c$'s as long as $0<m<n$. I don't see any patterns in that list.