Jacobsthal sum

In mathematics, Jacobsthal sums are finite sums of Legendre symbols related to Gauss sums. They were introduced by.

Definition
The Jacobsthal sum is given by
 * $$\phi_n(a)=\sum_{m\bmod p}\left(\dfrac{m(m^n+a)}{p}\right)$$

where p is prime and is the Legendre symbol.