Brewer sum

In mathematics, Brewer sums are finite character sum introduced by related to Jacobsthal sums.

Definition
The Brewer sum is given by
 * $$\Lambda_n(a) = \sum_{x\bmod p}\binom{D_{n+1}(x,a)}{p}$$

where Dn is the Dickson polynomial (or "Brewer polynomial") given by
 * $$ D_{0}(x,a)=2,\quad D_1(x,a)=x, \quad D_{n+1}(x,a)=xD_n(x,a)-aD_{n-1}(x,a)$$

and is the Legendre symbol.

The Brewer sum is zero when n is coprime to q2−1.