# how I would say the following summation

#### Bingk

How to say ....

Hi ... I'm doing a small presentation and I was wondering how I would say the following summation:

$$\sum_{0<i_1<...<i_n<p} \left(\frac{i_1}{3}\right) \frac{(-1)^{i_1}}{i_1 i_2 \cdot \cdot \cdot i_n}$$

where $\left(\frac{i_1}{3}\right)$ is the Legendre symbol, n is a positive odd integer and p is a prime such that p>n+1.

I'm not sure how to say the Legendre part ... would it be "the Legendre of i_1 over 3"?

Also, I'm not sure how I would say the summation part (the index) because it's not a straightforward from i=1 to p-1. It's a combination of unique (not equal) i's arranged in order, where 0<i<p.

Thanks, any help would be much appreciated :)

Last edited by a moderator:

#### fresh_42

Mentor
2018 Award
Looks good: the Legendre symbol $i_1$ over $3$ describes the first factor and the summation is over all possible combinations $0<i_1 < \ldots < i_n< p$ for a fixed $n$. If you also want to sum over $n$, then an additional $\sum_n$ is necessary.

"how I would say the following summation"

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