Hi, I was reading a thesis paper, and I guess I'm having problems with the notation.

n is a positive odd integer and p > n+1, p is a prime.

$\displaystyle \sum_{0<i_1<\cdot\cdot\cdot<i_n<p}(\frac{i_1}{3})\ frac{(-1)^{i_1}}{i_1 \cdot\cdot\cdot i_n} \equiv 0\ (mod\ p)$

$\displaystyle (\frac{i_1}{3})$ is the Legendre symbol

The above was given, but I can't get it to work ... and I think the indexes might be only those integers congruent to either 1 or 2 (mod 6), OR 4 or 5 (mod 6) (I got this part from reading the proof, you can read it at arxiv.org, do a math category search, journal reference 0904.1162, the title is "Some Curious Congruences Modulo Primes", by Li-Lu Zhao and Zhi-Wei Sun).

I'm pretty sure I don't know enough to figure out what's going on, but it looked like an interesting thesis, and I wanted to try and figure it out ... so if you could guide me to some reading material (preferably free and online ), or explain the notation, and any limitations on the indexes, that would be great.

Thanks in advance