Let $p$ be a prime number and $[p-1]=\{1, 2, \ldots, p-1\}$.
The following proposition is proved: (but I cannot find out where)
Proposition: The non-empty subset sums of $[p-1]$ are equally distributed $\pmod{p}$.
In other words, if $N(a)$ denotes the number of subset sums which are $\equiv a\pmod{p}$ then $N(a)=\frac{2^{p-1}-1}{p}$, for every integer $0\le a\le p-1$.
I know that there is a proof using $p$-th roots of unity (Complex numbers $z$, such that $z^p=1$), but I cannot find out where this is proved.
Can anybody give me some reference where I can find a proof of the proposition using complex numbers? I would prefer if possible some survey which also touches other similar topics and the techniques are based in complex numbers.
